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Books are Not to be taken from the Library Room.
Return this book on or before the
Latest Date stamped below.
University of Illinois Library
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EXPERIMENTAL SCIENCE SERIES FOR BEGINNERS. ,
mie) CRN ale:
‘SIMPLE, ENTERTAINING, AND INEXPENSIVE) EXPERI
MENTS ‘IN THE PHENOMENA OF SOUND,
FOR THE USE OF STUDENTS
“OF EVERY AGE,
BY
ALFRED MARSHALL MAYER, \%3«
“Professor of Physics in the Stevens Institute of Technology. Member of the
National Academy of Soiences ; of the American Philosophical Society,
Philadelphia; of the AmevicanAeg demy of Arts and Sciences,
Boston; of theNew-¥ 4 CAdEMYO, pdctences ; of the
German Ast j 0 American
Q vorgr ber -
oe dphitainolopledl ‘Sockety,
[RRARV \
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NEW YORK:
an APPLETON AND ocean aa
549 AND 551 BROADWAY.
1879.
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ty ats
rd
COPYRIGHT BY
ALFRED M. MAYER,
1878.
I DEDICATE
THIS BOOK TO MY GOOD FRIEND,
JOSEPH HENRY.
WHO INSPIRED MY YOUTH
WITH A LOVE OF
THE ART OF EXPERIMENTING,
i ie a ES ad
4
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5 CEP er hee et
PREFACE.
Tue books of the “Experimental Science Series for
Beginners” originated in the earnest and honest desire
to extend a knowledge of the art of experimenting, and
to create a love of that noble art, which has worked so
much good in our generation.
These books, though written for all those who love
experiments, and wish to know how to make them with
cheap and simple apparatus, will, it is hoped, be found
useful to teachers, and especially to the teachers and stu-
dents in our Normal Schools. The majority of those who
go from these schools will be called to positions where
only a small amount of money can be obtained for the
purchase of the apparatus needed in teaching science.
These little books will show how many really excellent
experiments may be made with the outlay of a few dol-
lars, a little mechanical skill, and—patience. This last
commodity neither I nor the school can furnish. The
teacher is called on to supply this, and to give it as his
share in the work of bringing the teaching of experimen-
tal science into our schools.
a laa PREFACE.
When the teacher has once obtained the mastery over
the experiments he will never after be willing to teach
without them ; for, as an honest teacher, he will know
that he cannot teach without them.
Well-made experiments, the teacher’s clear and sim-
ple language describing them, and a free use of the black-
board, on which are written the facts and laws which the
experiments show—these make the best text-books for
beginners in experimental science.
Teach the pupil to read Nature in the language of ex-
periment. Instruct him to guide with thoughtfulness the
work of his hand, and with attention to receive the teach-
ings of his eyes and ears. Books are well—they are in-
dispensable in the study of principles, generalizations, and
mathematical deductions made from laws established by
experiment—but, “Ce n’est pas assez de savoir les prin-
cipes, il faut savoir MANIPULER.”
Youths soon become enamored of work in which
their own hands cause the various actions of Nature to
appear before them, and they find a new delight in a
kind of study in which they receive instruction through
the doings of their hands instead of through the reading
of books. |
The object of this second book of the series is to show
how to make a connected series of experiments in Sound.
These experiments are to be made with the cheapest and
simplest apparatus that the author has been able to devise.
I have tried to be plain in giving directions for the con-
PREFACE. ty
struction and use of this apparatus. In my descriptions
of the experiments I have endeavored to be clear ; but in
this I may have failed. If I have, I am sure that the ex-
periments themselves are true, honest, and of good report,
and will supply all the shortcomings of language, which,
even from the best pens, gives but a weak and incomplete
conception of an experiment.
In Chapter II. is given an account of the order of the
experiments. These have’ been carefully selected, and
arranged so that one leads to the next. Each experiment
has been made by me over and over again, and the series
has been performed before me by beginners in the art. I
therefore know that they will all succeed if my directions
are perseveringly followed. The experiments are num-
bered in order up to 130, so that they may be referred to
from this work, and from the other books of the series.
Several of the instruments described are new, and
many of the experiments are so pleasing in their action
that they may be of interest to my scientific brethren, and
to those engaged with college classes. I would refer to
the instruments or experiments described in Experiments
1, 2, 17, 33, 34, 43 to 59, 61, 65, 66, 67, 68, 69, 70, 73, 74,
78, 79, 100, 104, 105, 107, 108, 110, 112, 121, 122, 125,
126, 127. }
A lively interest has recently been excited in the sub-
ject of Sound by two of the most remarkable inventions
of this century : Bell’s Telephone, and the Speaking and
Singing Phonograph of Mr. Thomas A. Edison. The first
8 PREFACE.
named of these inventions will be described in the fourth
book of the series ; the second I describe, with two ex-
cellent engravings, at the end of this volume.
The experiments have been completed for the remain-
ing books of the series, which will appear in the following
order (I. “ Light ;” I. “Sound,” already published) : III.
“Vision, and the Nature of Light ;” IV. “ Electricity
and Magnetism ;” V. “ Heat ;” VI. “Mechanics ;” VII.
“Chemistry ;” VIII. “The Art of Experimenting with
Cheap and Simple Instruments.”
Mr. Barnard, who was associated with me in writing
the book on “ Light,” found that his engagements did not
permit him to continue his work on the series.
Since the publication of “ Light” I have received the
request, from various parts of the country, that I should
make arrangements with some competent instrument-
maker, who will supply sets of apparatus to go with the
books of the series. This I have done, and Samuel
Hawkridge, instrument-maker to the Stevens Institute
of Technology, Hoboken, New Jersey, will supply the
sets of apparatus for “ Light ” and “Sound ” at the rates
given in his price-list at the end of this volume. The
separate pieces of the apparatus for “Sound” are num-
bered to correspond to the numbers of the experiments in
the book. By this plan the purchaser knows which pieces
of apparatus go together, and is also informed of their
uses. The student may find it cheaper to hunt up the
materials, and then make his own apparatus; but so
PREFACE. 9
many have desired to have the sets ready for use that I
have complied with their request. Of course it will be
understood that the instrument-maker must be paid for
the time taken in finding the objects in the market, and
for the labor and skill spent in making the apparatus,
and in packing it in convenient boxes.
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CON TENS.
PREFACE
CHAPTER I.
Introduction .
’ The Construction and tee of the Heliostat
/The Water-Lantern
CHAPTER ILI.
ON THE ORDER OF THE EXPERIMENTS IN THIS Book
CHAPTER III.
On THE NaTuRE oF SouND
CHAPTER IV.
On THE NaTuRE or Visratory MOTIONS
The Conical Pendulum
The Sand-Pendulum .
An Experiment which gives the Trace of a Vibrating Pine Rod
PAGE
24
27
The Pendular Motion reproduced from the Traces of the Pendulum
and of the Vibrating Rod .
Blackburn’s Double Pendulum
. Fixing the Curves of Blackburn’s eenaetonl on ihe :
Experiments in which the Motions of Two Vibrating Rods are made
_ to trace the Acoustic Curves .
The Way to draw the Acoustic Curves .
CHAPTER V.
On A VisratTine Soup, Liquip, or GasEous Bopy BEING ALWAYS
THE ORIGIN OF SOUND .
Experiments with a Tuning-Fork
Experiments with a Vibrating Tuning-Fork aie a Cork ‘Ball
12 CONTENTS.
PAGE
Experiments with a Brass Disk : : . ‘
Experiment in which a Submerged Flageolet is ifemed by forsigg
Water through it
Prof. Kundt’s Experiment, made with a Whistle and a Circnt Chimn-
ney, showing that, as in Wind Instruments, a Vibrating Column
of Air may originate Sonorous Vibrations
CHAPTER VI.
ON THE TRANSMISSION OF SONOROUS VIBRATIONS THROUGH SOLIDS,
Liquips, AND GASES, LIKE AIR
Experiment with a Tuning-Fork and Wooden Rod :
Experiment in which Sonorous Vibrations are sent through Water
Experiments showing that the Air is constantly vibrating while
Sonorous Vibrations are passing through it
Experiments with the Sensitive-Flames of Govi and Barry, aa of
Geyer
CHAPTER VII.
On THE VELOCITY OF TRANSMISSION OF Sonorous VIBRATIONS, AND
ON THE MANNER. IN WHICH THEY ARE PROPAGATED THROUGH
Exastic Bopres
On the Speed with which soneriid Winestete Rees
Experiments with Glass Balls on a Curved Railway
Experiments with a Long Brass Spring, showing how viorelacus are
transmitted and reflected :
Explanation of the Manner in which Saiseees Vibrations are prop-
agated
Experiments with Crova’ s Disk, shorire how Sanvions Vibration:
travel through Air and other Elastic Matter
CHAPTER VIII.
On tHE INTERFERENCE OF Sonorous VIBRATIONS AND ON THE
Beats or Sounp
Experiments in Interference of Sound penie with a Trainee ork and
a Resounding-Bottle
Experiments in which Interference of Bound is ebieined with a Fork
and Two Resounding-Bottles
Experiment showing Reflection of Sound ee a Flat ae Fant 3
66
69
70
73
73
74
75
80
84
84
85
87
89
91
98
102
102
104
CONTENTS. 13
PAGE
Experiments in which, by the Aid of a Paper Cone and a Rubber
Tube, we find out the Manner in which a Disk vibrates. 105
Experiments with Beating Sounds . 5 : a . 106
CHAPTER. IX.
On THE REFLECTION oF Sound . : . 110
Prof. Rood’s Experiment, showing the eflestion of Sound ne a
CHAPTER X.
On THE Prrcu or Sounps . ae A ale « : 113
Experiments with the Siren . : : a hie
Experiment with the Siren, in which is found the amber of Vibra-
tions made by a Tuning-Fork in one Second F 118
On finding the Velocity of Sound with a sa Fork and a Rea:
nant Tube ‘ 120
On the Relative Numbers we Vabcone per ven d given ns Phan
Pipes of Different Length . ; ; ‘ P 122
CHAPTER XI.
On tne Formation or THE Gamur. : 124
Experiments with the Siren, showing how the Sounds of the Gamut
are obtained : ~ : : 4 : 124
CHAPTER XII.
EXPERIMENTS WITH THE SONOMETER, GIVING THE SOUNDS OF THE
GAMUT AND THE HaRMONICS . eked
Experiments with the Sonometer, giving the Heeachic Sanncé 132
Prof. Dolbear’s Method of making Melde’s Experiments on Vibrating
Cords ‘ ; 5 : ‘ : : 135
CHAPTER XIII.
ON THE INTENSITIES OF SOUNDS. 137
Experiment showing that as the Swings ofa eciheting Bout cone
less the Sound becomes feebler - . : : ; 137
CHAPTER XIV.
On Co-VIBRATION. . P é . “ty 439
Experiments with Two ening. Tarks , ‘ 139
Experiments on the Co-vibration of Two Wires in the Renagmiee 140
Experiment of swinging a Heavy Coal-Scuttle by the Feeble Pulls
of a Fine Cambric Thread j ‘ : ‘ . 144
14 CONTENTS.
CHAPTER XV.
On THE CHANGES IN THE Pitcu oF A. VIBRATING BopDy CAUSED BY ITS
Mortron .
Experiment in mich the Pitch of a Whistle} is ehaned By Aare
it round in a Circle : . .
CHAPTER XVI.
ON THE QUALITY OF SOUNDS : A ‘
Experiments on the Quality of Sounds .
CHAPTER XVII.
ON THE ANALYSIS AND SYNTHESIS OF Sounps
An Experimental Analysis of the Compound Sounds of a Pato
Experiments in which we make Compound Sounds of Different
Qualities by combining Various Simple Sounds :
How the Ear analyzes a Compound Sound into its Simple Sounds
An Experiment which shows the Motion of a Molecule of Air, when
it is acted on by the Combined Vibrations of Six Harmonics .
Experiments in which Compound Sounds are analyzed by viewing
in a Rotating Mirror the Vibrations of Kénig’s Manometric
Flames
Terquem’s Experiment, which Kendens aihis the Motions of | a Vi-
brating Disk
CHAPTER XVIII.
ON HOW WE SPEAK, AND ON THE TALKING MACHINES or FABER AND
EpIson
How we speak
Experiments in which a Toy Tritt pet dais, and a Spchbing
Machine is made
Faber’s Talking Machine
Edison’s Talking Phonograph
CHAPTER XIX.
On Harmony anp Discorp: A SHORT EXPLANATION OF WHY SOME
NOTES, WHEN SOUNDED TOGETHER, CAUSE AGREEABLE AND OTHERS
DISAGREEABLE SENSATIONS
Price-List or Apparatus For “Ligur” anp “Sounp”
PAGE
143
143
145
145
148
148
150
152
153
156
163
(165
165
167
170
170
175
180
p>.
Up
CHAPTER I.
Pe ir ks OL EAC 1 T ONs,
To know how the various sounds of Nature and of
music are made ; to understand the action of the mechan-
ical contrivances in our throat and ears, with which we
speak and hear ; to be able to explain the cause of the
different tones of musical instruments ; to know why cer-
tain notes sounded together give harmony, while others
make discord : such knowledge is certainly valuable, cu-.
rious, and interesting. You may read about these things,
but a better way is to study the things themselves, by
_making experiments, and these experiments will tell you
better than books about the causes and the nature of
sounds.
To make an experiment means to put certain things
in relation with certain other things, for the purpose of -
finding out how they act on each other. An experiment
is, therefore, a finding out.
It is the aim of this book to show you how to construct
your own apparatus out of cheap and common things, and
to aid you in becoming an experimenter. The student
should, with patience and thoughtfulness, make each ex-
16 SOUND.
periment in order, for they have been arranged so that
one leads naturally to the making and understanding of
the next. If the first, second, or even third trial does not
give success, do not be discouraged, for the oldest and
most gifted experimenters often fail ; yet they have made
noble discoveries in science by their experiments, because
they had patience and perseverance, as well as skill and
knowledge. Do not be disheartened, and you will become
a skillful experimenter.
In making an experiment, we may work alone, or we
may perform the work in the company of our friends, so
that a large number may see what we do, and assist in
making the experiment. To exhibit an experiment on a
large scale, so that all the people in a room may see it, we
need a magic-lantern. A lantern with a good artificial
light will cost a great deal of money, but by using the
water-lantern and heliostat, described in the first book of
this series, and employing the sun for a light, we can ex-
hibit many of our experiments in sound, in the most beau:
tiful manner, before a large company, and at a trifling
expense. |
At the same time, the lantern is not essential, and if
you do not wish to use it you can perform all of the ex-
periments without its aid.
THE HELIOSTAT.
The word “heliostat” is formed of two Greek words—
helios, the sun, and statos, standing. There is an instru-
ment so named, because it keeps a reflected beam of
sunlight constantly pointing in the same direction. In
“Light,” the first book of this series, we have given a de-
scription of a simple heliostat ; but, as some of our readers
may not have that volume, we here give a short descrip-
INTRODUCTION.
mmm wenn ne mene sera =-
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Fra. 1.
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17
18 SOUND.
tion of the manner of making and using that instrument :
The sun, in his daily apparent path through the sky,
moves as though he were fixed to the surface of a vast
globe, which makes a daily revolution around an axis.
This axis is found by drawing a line from a point near the
pole-star to the centre of the earth, and then continuing
S.
lice.
Pes)
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Sols
Mi or af Winler >
9/6 6" Movaste Mirror.
6X 5/2" StationanyMirror
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Fia. 2.
‘this line beyond the earth till it meets the heavens in a
spot which can be pointed out only by those who live
south of the earth’s equator. This line is the axis around
which the sphere of the heavens appears to revolve once
inaday. The knowledge of this motion of the sun ena-
bles us to construct an instrument with a movable mirror
a
INTRODUCTION. 19
which will reflect his beams in one direction from sunrise
to sunset.
Figs. 1 and 2 are drawings of the heliostat. The
scale at the bottom of Fig. 1 gives in inches the size of
the parts of the lower drawing. -H is a round wooden
rod, which we call the polar axis of the heliostat, because
it points toward the pole-star when the instrument is in
the proper position for use. This axis turns freely in a
hole in the board A B, and in the block AK. A wooden
washer MY, which is slid over the axis and is fastened to it,
rests on the block A, and thus keeps the axis from slip-
ping down. The end # of the axis has a slot cut in it,
and a semicircle of wood G', which is screwed to the back
of a board carrying the mirror J, turns in this slot around
a carriage-bolt, as shown in the figure. This movable
mirror is fastened to the board either by strings or by
elastic bands, which go around the ends of the board and
mirror. ‘The mirror should be of silvered glass, not of
common looking-glass. It is, as stated in Fig. 2, 9$ inches
long and 6 inches wide.
Since the sun in his daily course through the heavens
appears to move as though attached to the surface of a
sphere, which revolves on an axis parallel to the polar axis
of the heliostat, it follows that, if we tilt the mirror V
so that the sunbeam which strikes it is reflected down-
ward in the direction of the polar axis H, then, by simply
turning this axis with the sun.as he moves in the sky, we
can keep his rays constantly reflected in that direction.
The dotted line and arrow going from the mirror V to O
show the direction of the reflected rays. But this is not
a convenient direction in which to have the sunbeam, so we
fix at O another mirror, 6 inches high and 54 inches wide,
which reflects the beam from O to B, through a hole of 5
20 SOUND.
inches diameter cut in the board A B. Brackets, 14 x 12
inches, with their 12-inch sides screwed to the board A B,
support a shelf D, which holds the mirror 0.
Each morning in the year the sun appears on the. hori-
zon at a different point on the celestial sphere, so that on
different days we have to give the mirror WV a different
tilt toward thesun. At the equinoxes, that is, on the 20th
day of March and September, the rays fall at right an-
gles to the axis HZ, as shown in Figs. 1 and 2, and the
mirror in Fig. 1 is placed at the proper tilt for those days.
In Fig. 2 the tilt of the mirror is also given for the days
of the summer and winter solstices.
As we go north, say to Boston, the north star rises to
a greater height above the horizon, so the axis of our
heliostat at Boston must stand more upright than at New
York, and have the position marked “ 42° 22’, Boston.”
Going south, say to New Orleans, we shall see the pole-star
shining above the horizon, at a height which is one-fourth
less than the height it appears at in New York ; therefore,
at New Orleans, the polar axis of the heliostat is lowered
into the position marked “29° 58'’, New Orleans.” So
we see that in different latitudes the axis of our heliostat
has to be placed at different angles with the horizontal
line. In order that the instrument may work correctly,
the angle which it should make with the horizon is the
same as the latitude of the place. These are the angles
written before the places named in Fig. 2. These changes
in the slant of the polar axis for different latitudes need
like changes in the shape of the block A’; but if one first
draws the correct line in which the axis goes through the
board A B, the block # can be formed without trouble.
ExPERIMENT 1.—To place the heliostat in position for
use, we raise the sash of a southern window, and secure
INTRODUCTION. 21
the board A B between its jambs, with the mirrors out-
side and the polar axis inside the room. With a shawl or
blanket closely cover that part of the window above the
board A B, so as to keep out all light except what comes
into the room through the hole B. The movable mirror
is now turned toward the sun, and tilted so that the beam
from it is reflected by the fixed mirror O into a horizontal
direction, and at right angles to the board A B. If the
window faces the south the heliostat will work with entire
success. If the window does not truly face the south, then
the board A B should be tilted sideways till it does face
that direction, and any opening thus made between the
board A £ and the window-sash may be closed with a
strip of wood.
THE WATER-LANTERN.
Tig. 3 represents a wooden box containing a mirror
placed inside at an angle of 45°, and supported by wood
slats fastened to the sides of the box. The side of the box
opposite the mirror is open. In the top of the box is a
round hole 5 inches (12.7 centimetres) in diameter. In
this hole rests a hemispherical glass dish, 53 inches (14
centimetres) in diameter, made by cutting off the round
top of a glass shade. At the back of the box is a wooden
slide carrying a horizontal shelf on its top. This slide has
a long slot cut in it, and, by means of a bolt and nut fas-
tened to the back of the box, it can be made fast at any
required height. This slide is 16 inches (40.6 centimetres)
long, 5 inches (12.7 centimetres) wide, and # inch (19 mil-
limetres) thick. The shelf is 7 inches (17.8 centimetres)
long and 5 inches (12.7 centimetres) wide, and has a hole
34 inches (8.8 centimetres) in diameter cut in its centre.
A block of wood is fastened to the back of the box in the
22
ai
Ht
slot, to serve as a guide in raising and lowering the slide
which carries the lens. On the hole in the shelf rests a large
INTRODUCTION. 23
watch-glass, or shallow dish, about 4 inches (10.1 centi-
metres) in diameter. A plano-convex lens may be used
in its place. On each side of the shelf are two upright
wooden arms, and on screws, which go through them, is —
swung a looking-glass, 7 inches (17.8 centimetres) long
and 4 inches (10.1 centimetres) wide.
ExpPERIMENT 2.—Place this lantern before the helio-
stat, so that the full beam of light will be reflected from
the mirror upward through the glass bowl and the watch-
glass.’ Fill each of these with clear water, and then place
the swinging mirror at an angle of 45°. Hang up a large
screen of white cotton cloth, or sheet, in front of the lan-
tern, and from 15 to 40 feet (4.5 to 12.2 metres) distant.
On this screen will appear a circle of light projected from
the lantern. Get a piece of smoked glass, and trace upon
it some letters, and then lay it on the water-lens. The
image of the letters will appear on the screen, in white on
a black ground. If they are not distinct, loosen the nut
at the back of the box, and move the wooden slide up or
down till the right focus is obtained.
This water-lantern may now be used for all the work
_ performed with ordinary magic-lanterns. Place a sheet
of clear glass over the large lens, to keep the dust out of
the water, and then you can lay common lantern-slides on
this as in a magic-lantern. |
1 Dr. R. M. Ferguson first used a condensing lens made of a glass
shade filled with water. See Quarterly Journal of Science, April, 1872.
Subsequently, Professor Henry Morton made a watch-glass filled with
water, or other liquid, serve for the projecting lens of the lantern.
2
24 SOUND.
Oe Py AOELA ERY OL
ON THE ORDER OF THE EXPERIMENTS IN: THIS
BOOK.
In Chapter I. are explained the construction and use of
the heliostat and water-lantern. In Chapter IV. we begin
by experimenting on the three ways in which a body may
vibrate. We show that it may swing to and fro like a
pendulum ; that it may vibrate by shortening and length-
ening ; and that it may vibrate by twisting and untwist-
ing itself. Then we study the nature of vibratory motions,
and find that they are like the motion of a swinging pen-
-dulum ; and the motion of the pendulum we discover is
exactly like the apparent motion of a ball looked at in the
direction of the plane of a circle, in which it revolves with
a uniform velocity.
We then, in Chapter V., experiment on those vibra-
tions whose frequency is so great that they cause sound ;
and show, in this and the next chapter, that whenever we
perceive a sound some solid, liquid, or gaseous body is in
a state of rapid vibration, and that these vibrations go
from the vibrating body to the ear through a solid, liquid,
or gas—air being generally the medium which transmits
the vibrations. These vibrations, acting on the ear, make
the auditory-nerve fibrils tremble, and thus is caused the
sensation of sound.
ORDER OF THE EXPERIMENTS. Q5
In Chapter VIII. are experiments which show how
these vibrations are transmitted through solids, liquids,
and gases, to a distance from the source of the sound.
The knowledge of how the sonorous vibrations travel
through the air leads to experiments in which we make
two sonorous vibrations meet, and, by their mutual action,
or interference, cause rest in the air and silence to the
ear. This silence may be continuous, or it may be of short
duration alternating with sound, and in this case we have
“beats.”
Chapter IX. gives Professor Rood’s very striking ex-
periment showing the reflection of sound. In Experi-
ment No. 73, of Chapter VIIL, I show how we may read-
ily obtain reflection of sound from a gas-flame.
In Chapter X. we give experiments with a siren made
of card-board, and with it show that the pitch of sounds
. rises with the frequency of the vibrations causing them.
With the same siren, in connection with a resonant tube
tuned to a tuning-fork, we determine the number of vibra-
tions the fork makes in asecond. With the same tube and
fork we then measure the velocity of sound in air. With
the same siren, in Chapter XI., the experimenter finds
that the notes of the gamut are given by a series of vibra-
tions whose numbers per second bear to one another cer-
tain fixed numerical relations.
In Chapter XII. we experiment with a cheap so-
nometer, and find the law which connects the length
of a string with the frequency of its vibrations ; then,
with this law in our possession, we make the sonometer
give all the notes of the gamut and the sounds of the har-
monic series.
In Chapters XIII, XIV., and XV., are described ex-
periments showing the cause of the varying intensities of
26 « SOUND.
sounds, experiments on the sympathetic vibrations of
bodies, and on the change made in the pitch of a sounding
body by moving it. -
The cause of the different quality of sounds is explained
in Chapter XVI., and then follow, in Chapter X VIL, ex-
periments on the analysis of compound sounds, and on the
formation of compound sounds by sounding together the
simple sounds which compose them. In this chapter is
also found an experiment in which is reproduced the mo-
tion of a molecule of air when it is acted on, at the same
time, by the vibrations giving the first six harmonics of a
compound sound ; also, directions for making a very sim-
ple form of Kénig’s vibrating flame, and a cheap revolving
mirror in which to view the flame.
Chapter X VIII. .contains experiments on the voice in
talking and singing. After explaining how we speak, I
give experiments on the resonance of the oral cavity, and
then show how a toy trumpet can be made to speak, and
a talking machine made out of the trumpet and an orange.
This chapter concludes with accounts of the talking ma-
chine of Faber, of Vienna, and of the recently invented
talking and singing machine of ‘Mr. Edison, which is in-
deed the acoustic marvel of the century.
Chapter XIX. concludes the book, and gives a short
explanation of the causes of harmony and discord.
NATURE OF SOUND. 27
CHAPTER III.
ON THE NATURE OF SOUND.
SOUND is the sensation peculiar to the ear. This sen-
sation is caused by rapidly succeeding to-and-fro motions
of the air which touches the outside surface of the
drum-skin of the ear. These to-and-fro motions may
be given to the air by a distant body, like a string of a
violin. The string moves to and fro, that is, it vibrates.
These vibrations of the string act on the bridge of the
violin, which rests on the belly or sounding-board of the
instrument. The surface of the sounding-board is thus
set trembling, and these tremors, or vibrations, spread
through the air in all directions around the instrument,
somewhat in the manner that water-waves spread around
the place where a stone has been dropped into a quiet pond.
These tremors of the air, however, are not sound, but the
cause of sound. Sound, as we have said, is a sensation ;
but, as the cause of this sensation is always vibration, we
call those vibrations which give this sensation sonorous
vibrations. Thus, if we examine attentively the vibrat-
ing string of the violin, we shall see that it looks like a
shadowy spindle, showing that the string swings quickly
to and fro ; but, on closing the ears, the sensation of sound
disappears, and there remains to us only the sight of the
quick to-and-fro motion which, the moment before, caused
the sound.
28 SOUND.
Behind the drum-skin of the ear is a jointed chain of
three little bones. The one, # of Fig. 4, attached to the
drum-skin, is called the hammer ,; the next, A, is called
the anvil ; the third, S, has the exact form of a stirrup,
and is called the stirrup-bone. This last bone of the chain
is attached to an oval membrane, which is a little larger
than the foot of the stirrup. This oval membrane closes
Fie. 4.
a hole opening into the cavity forming the inner ear ; a
cavity tunneled out of the hardest bone of the head, and
having a very complex form. The oval hole just spoken
of opens into a globular portion of the cavity, known as
the vestibule, and from this lead three semicircular ca-
nals, SC, and also a cavity, C, of such a marked resem-
NATURE OF SOUND. 29
blance to a snail’s shell that it is called cochlea, the Latin
word for that object. The cavity of the inner ear is filled
with a liquid, in which spread out the delicate fibres of
the auditory nerve.
Let us consider how this wonderful little instrument
acts when sonorous vibrations reach it. Imagine the
violin-string vibrating 500 times in one second. The
sounding-board also makes 500 vibrations in a second.
The air touching the violin is set trembling with 500
tremors a second, and these tremors speed with a velocity
of 1,100 feet in a second in all directions through the sur-
rounding air. ‘They soon reach the drum-skin of the ear.
The latter, being elastic, moves in and out with the air
which touches it. Then this membrane, in its turn,
pushes and pulls the little ear-bones 500 times in a second.
The last. bone, the little stirrup, finally receives the vibra-
tions sent from the violin-string, and sends them into the
fluid of the inner ear, where they shake the fibres of -the
auditory nerve 500 times in a second. These tremors of
the nerve—how we know not—so affect the brain that we
have the sensation which we call sound. The description
we have just given is not that of a picture created by the
imagination, but is an account of what really exists, and
of what can actually be seen by tue aid of the proper
instruments.
A body may vibrate more or less frequently in a sec-
ond ; it may swing over a greater or less space; and it
may have several minute tremors while it makes its main
swing. These differences in vibrations make sounds higher
or lower in pitch, loud or soft, simple or compound. It is
easy to say all this, but really, to understand it, one must
make experiments and discover these facts for himself.
30 SOUND.
CHAPTER IV.
ON THE NATURE OF VIBRATORY MOTIONS.
Tue character of a sound depends on the nature of the
vibrations which cause it, therefore our first experiments
will be with vibrations which are so slow that we can
study the nature of these peculiar motions. These experi-
ments will be followed by others on vibrations of the same
kind, only differing in this—that they are so rapid and
frequent that they cause sounds. A correct knowledge of
the nature of these motions lies at the foundation of a
clear understanding of the nature of sound. We hope
that the student will make these experiments with care,
and keenly observe them.
EXPERIMENT 3.—At the toy-shops you can buy for a
few cents a wooden ball having a piece of elastic rubber
fastened to it. Take out the elastic and lay it aside, as
we shall need it in another experiment. Get a piece of fine
brass wire, about 2 feet (61 centimetres) long, and fasten
it to the ball. The weight.of the ball should pull the wire
straight, and, if it does not, a finer wire must be used.
Hold the end of the wire in the left hand, and with the
right hand draw the ball to one side. Let it. go, and it
will swing backward and forward like the pendulum of a
clock. This kind of movement we call a pendulous or
transverse vibration.
NATURE OF VIBRATORY MOTIONS. 31
EXPERIMENT 4.—Cut out a narrow triangle of paper,
4 inches (10 centimetres) long, and paste it to the bottom
of the ball. Twist the wire which supports the ball by
turning the latter half round, and watch the paper pointer
as it swings first one way and then the other. Here we
have another kind of vibration, a motion caused by the
twisting and untwisting of the wire. Such a motion is
called a torsional vibration. |
Exprrimment 5.—Take off the wire and the paper and
put the elastic on the ball. Hold the end of the elastic in one
hand, and with the other pull the ball gently downward,
then let it go. It vibrates up and down in the direction
of the length of the elastic. Hence we call this kind of
motion a longitudinal vibration.
These experiments show us the three kinds of vibra-
tions, transverse, torsional, and longitudinal. They differ
in direction, but all have the same manner of moving; for
the different kinds of vibration, transverse, longitudinal,
and torsional, go through motions with the same changes in
velocity as take place in the swings of an ordinary pendu-
lum. These vibrations all start from a position of momen-
tary rest. The motion begins slowly, and gets faster and
faster till the body gains the position it naturally has when
it is at rest—at this point it has its greatest velocity.
Passing this point, it goes slower and slower till it again
comes momentarily to rest, and then begins its backward
motion, and repeats again the same changes in velocity.
It is now necessary that the student should gain clear
ideas of the nature of this pendulous motion. It is the
cause of sound. It exists throughout all the air in which
a sound may be perceived, and, by the changes in the num-
ber, extent of swing, and combinations of these pendular
motions, all the changes of pitch, of intensity, and of quality
32 SOUND.
of sound are produced. Therefore, the knowledge which
we now desire to give the reader lies at the very founda-
tion of a correct understanding of the subject of this
book.
An experiment is the key to this knowledge. It is the
experiment with
THE CONICAL PENDULUM.
An ordinary pendulum changes its speed during its
swings right and left exactly as a ball appears to change
its speed when this ball revolves with a uniform speed in
a circle, and we look at it along a line of sight which
is in the plane of the circle.
ExpPERIMENT 6.—Let one take the ball and wire to
the farther end of the room, and by a slight circular mo-
tion of the end of the wire cause the ball to revolve in a
circle. Soon the ball acquires a uniform speed around the
circle, and then it forms what is called a conical pendu-
lum; a kind of pendulum sometimes used in clocks. Now
stoop down till your eye is on a level with the ball.
This you will know by the ball appearing to move from
side to side tm a straight line. Study this motion care-
fully. It reproduces exactly the motion of an ordinary
pendulum of the same length as that of the conical pendu-
lum. From this it follows that the greatest speed reached
during the swing of an ordinary pendulum just equals the
uniform speed of the conical pendulum. That the appar-
ent motion you are observing is really that of an ordinary
pendulum, you will soon prove for yourself to your entire
satisfaction; and here let me say that one principle or
fundamental fact seen in an experiment and patiently re-
flected on is worth a chapter of verbal descriptions of the
same experiment.
NATURE OF VIBRATORY MOTIONS. 30
Suppose that the ball goes round the circle of Fig. 5
in two seconds; then, as the circumference is divided into 16
equal parts, the ball moves from 1 to 2, or from 2 to 3, or
from 3 to 4, and so on, in one-eighth of a second. But to
the observer, who looks at this motion in the direction of the
plane of the paper, the ball appears to go from 1 to 2, from
is 16 9 8 4% 6;
Fia. 5.
2 to 3, from 3 to 4, etc., on a line A B, while it really
goes from 1 to 2, from 2 to 3, from 3 to 4, ete., in the cir-
cle, - The ball when at 1 is passing directly across the line
of sight, and, therefore, appears with its greatest velocity;
but when it is in the circle at 5 it is going away from the
observer, and when at 13 it 1s coming toward him, and,
therefore, although the ball is really moving with its regu-
lar speed when at 5 and 13, yet it appears when at these
points momentarily at rest. From a comparison of the
similarly numbered positions of the ball in the circle and
on the line A JB, it is evident that the ball appears to go
from A to B and: from B back to A in the time it takes to
go from 13, round the whole circle, to 13 again. That is,
the ball appears to vibrate from A to B in the time of one
second, in which time it really has gone just half round
ae SOUND.
the circle. A comparison of the unequal lengths, 13 to 12,
12 to 11, 11 to 10, ete., on the line A #B, over which the
ball goes in equal times, gives the student a clear idea
of the varying velocity of a swinging pendulum.
THE SAND-PENDULUM.
£ Nt
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Tih
FG. 6.
Fig. 6 represents an upright frame of wood standing
on a platform, and supporting a weight that hangs by a
cord. A A is a flat board about 2 feet (61 centimetres)
long and 14 inches (35.5 centimetres) wide. .b B are
two uprights so high that the distance from the under
NATURE OF VIBRATORY MOTIONS. 35
side of the cross-beam ( to the platform A A is exactly
41,1, inches (1 metre and 45 millimetres). The cross-beam
Cis 18 inches (45.7 centimetres) long. At D is a wooden
post standing upright on the platform. Get a lead disk,
or bob, 3,3; inches (8 centimetres) in diameter and 2 inch
(16 millimetres) thick. In the centre of this is a hole 1
inch (25 millimetres) in diameter. This disk may easily
be cast in sand from a wooden pattern. , At the tinner’s
we may have made a little tin cone 1-3, inch (80 milli-
metres) wide at top and 24 inches (57 millimetres) deep,
and drawn to a fine point. Carefully file off the point
till a hole is made in the tip of the cone of about =; inch
in diameter. Place the tin cone in the hole in the lead
disk, and keep it in place by stuffing wax around it. A
glass funnel, as shown in the figure, may be used instead
of the tin cone. With an awl drill three small holes
through the upper edge of the bob at equal distances from
each other. To mount the pendulum, we need about 9 feet
(271.5 centimetres) of fine strong cord, like trout-line.
Take three more pieces of this cord, each 10 inches (25.4
centimetres) long, and draw one through each of the holes
in the lead bob and knot it there, and then draw them to-
gether and knot them evenly together above the bob, as
shown in the figure. On the cross-bar, at the top of the
frame, is a wooden peg shaped like the keys used in a
violin. ‘This is inserted in a hole in the bar—at /’in the
figure. Having done this, fasten one end of the piece of
trout-line to the three cords of the bob, and pass the other
end upward through the hole marked /’, then pass it
through the hole in the key 7’; turn the key round several
times; then pass the cord through the hole at G, to the bob,
and fasten it there to the cords. Then get a small bit of
copper wire and bend it once round the two cords just
36 SOUND.
above the knot, as at 7 in the figure. This wire ring, and
the upright post at the side of the platform, we do not need
at present, but they will be used in future experiments
with this pendulum,
Tack on the platform A A a strip of wood Z. This
serves as a guide, along which we can slide the small board
m, on which is tacked a piece of paper.
ExPERIMENT 7.—F ill the funnel with sand, and, while
the pendulum is stationary, steadily slide the board under
it. The running sand will be laid along ZW, Fig. 7, in
a straight line. If the board was slid under the sand dur-
ing exactly two seconds of time, then the length of this
line may stand for two seconds, and one-half of it may
stand for one second, and so on. ‘Thus, we see how time
may be recorded in the length of a line.
- Brush off the heaps of sand at the ends of the line, and
bring the left-hand end of the sand-line directly under the
point of the funnel, when the latter is at rest. Draw the
lead bob to one side, to a point which is at right angles
b C
Fig. 7.
to the length of the line, and let it go. It swings to and
fro, and leaves a track of sand, @ 6, which is at right an-
gles to the line Z UY, Fig. 7.
NATURE OF VIBRATORY MOTIONS. 37
Suppose that the pendulum goes from a to }, or from
6 to a, in one second, and that, while the point of the fun-
nel is just over L, we slide the board so that, in two sec-
onds, the end 1 of the line Z M comes under the point
of the funnel. In this case, the sand will be strewed by
the pendulum to and fro, while the paper moves under it
through the distance Z MZ. The result is, that the sand
appears on the paper in a beautiful curve, Z C NV D MM.
Half of this curve is on one side of Z MY, the other half
on the opposite side of this line.
The experimenter may find it difficult to begin moving
the paper at the very instant that the mouth of the funnel
is over Z ; but, after several trials, he will succeed in do-
ing this. Also, he need not keep the two sand-lines, Z IZ
and a 6, on paper during these trials; he may as well
use their traces, made by drawing a sharply-pointed pencil
through them on to the paper.
By having a longer board, or by sliding the board
slowly under the pendulum, a trace with many waves in
it may be formed, as in Fig. 8.
Fi¢. 8.
As the sand-pendulum swung just like an ordinary
pendulum when it made the wavy lines of Figs. 7 and 8, it
follows that these lines must be peculiar to the motion of
a pendulum, and may serve to distinguish it. If so, this
curve must have some sort of connection with the motion
of the conical pendulum, described in Experiment 6.
This is so, and this connection will be found out by an
attentive study of Fig. 9.
38 SOUND.
In this figure we again see a
wavy curve, under the same circu-
lar figure which we used in explain-
ing how the motion of an ordinary
pendulum may be obtained from
the motion of a conical pendulum.
This wavy curve is made directly
from measures on the circular fig-
ure, and certainly bears a striking
resemblance to the wavy trace made
by the sand-pendulum in Experi-
ment 7. You will soon see that to
prove that these two curves are
precisely the same, is to prove that
the apparent motion of the conical
pendulum is exactly like the mo-
tion of the ordinary pendulum.
Thé wavy line of Fig. 9 is thus
formed: The dots on A B, as al-
ready explained, show the appar-
ent places of the ball on this line,
when the ball really is at the points
correspondingly numbered on the
circumference of the circle. With-
out proof, we stated that this ap-
parent motion on the line A B was
exactly like the motion of a pen-
dulum. ‘This we must now prove.
The straight line Z I is equal to
the circumference of the circle
stretched out. It is made thus: We
take in a pair of dividers the dis-
tance 1 to 2, or 2 to 3, etc., from the circle, and step this
e 2 ——@
we
M15 I
NATURE OF VIBRATORY MOTIONS. 39
distance off 16 times on the line ZW, hence Z M
equals the length of the circumference of the circle. In
time this length stands for two seconds, for the ball in
Experiment 6 took two seconds to go round the circle.
This same length, you will also observe, was made in the
same time as the sand-line Z M/ was made in Experiment 7.
_In Fig. 9 the length Z WV, of two seconds, is divided into 16
parts ; hence each of them equals one-eighth of a second,
just as the same lengths in the circle equal eighths of a
second. ‘Thus the line L WM of Fig. 9, as far as a record
of time is concerned, is exactly like the sand-line L M of
Experiment 7, and the line A B of Fig. 9, in which the
ball appeared to move, is like the line a 0 of Fig. 7, along
which the sand-pendulum swung.
Now take the lengths from 1 to 2,1 to 3,1 to 4, 1 to 5,
and so on, from the line A B of Fig. 9, and place these
lengths at right angles to the line Z WW at the points 1, 2,
3, 4, 5, and so on; by doing so, we actually take the dis-
tances at which the ball appeared from 1 (its place of
greatest velocity), and transfer them to Z 17, therefore,
these distances correspond to the distances from Z WV,
Fig. 7, to which the sand-pendulum had swung at the end
of the times marked on LZ @ of Fig. 9.
Join the ends of all these lines, 2 2’, 3 3’, 4 4’, ete., by
drawing a curve through them, and we have the wavy
line of Fig. 9. :
This curve evidently corresponds to the curve Z O NV
D M of Fig. 7 made by the sand-pendulum ; and it must
be evident that, if this curve of Fig. 9 is exactly like the
curve traced by the sand-pendulum in Experiment 7, it
follows that the apparent motion of the conical pendulum,
as seen in the plane in which it revolves, is exactly like
the real motion of an ordinary pendulum,
40 SOUND.
ExPERIMENT 8.—To test this, we make on a piece of
paper one of the wavy curves exactly as we made the one
in Fig. 9, and we tack this paper on the board L WM of
the sand-pendulum, being careful that when the board is
slid under the stationary pendulum the point of the fun-
nel goes precisely over the centre line Z M (Fig. 9) of
the curve.
Now draw the point of the funnel aside to a distance
from the line Z M equal to one-half of A B, or, what is the
same, from 5 to 5’ of Fig. 9. Pour sand in the funnel, and
let the bob go. At the moment the point of the funnel is
over Z, slide the board along so that, when the point of
the funnel comes the third time to the line Z J, it is at
the end © of this line. This you may not succeed in
doing at first, but after several trials you will succeed,
and then you will have an answer from the pendulum as to
the kind of motion it has, for you will see the sand from
the swinging pendulum strewed precisely over the curve
you placed under it. Thus you have conclusively proved
that the apparent motion of the conical pendulum, along
the line A S, is exactly like the swinging motion of an
ordinary pendulum.
As it is difficult to start the board with a uniform mo-
tion at the very moment the pendulum is over the line
LL M, it may be as well to tack a piece of paper on the
board with no curve drawn on it, and then practise till
you succeed in sliding the board under the pendulum,
through the distance Z MV, in exactly the time that it
takes the pendulum to make two swings. Now, if you
have been careful to have had the swing of your pendu-
lum just equal to A #, or from 5 to 5’ on the drawing of
the curve, you will have made a curve in sand which is
precisely like the curve you have drawn ; for, if you trace
NATURE OF VIBRATORY MOTIONS. Al
the sand-curve on the paper by carefully drawing through
it the sharp point of a pencil, and then place this trace
against a windew-pane with the drawing of the curve,
Fig. 9, directly over it, you will see that one curve lies
directly over the other throughout all their lengths.
This curve, which we have made from the circle in
Fig. 9, and have traced in sand by the pendulum, is called
the curve of sines, or the sinusoid. It is so called because
itis formed by stretching the circumference of a circle
out into a line, and then dividing this line, Z © of Fig. 9,
into any number of equal parts. From the points of these
divisions, 1, 2, 3, 4, 5, ete., of Z MW, we erect perpendicu-
lars, 2 2’, 3 3’, 4 4’, 5 5’, etc., equal to the lines a 2,
b 3, ¢ 4, d 5, etc., in the circle. These lines in the cir-
cle are called sines ; so, when we join the ends of these
lines, erected to the straightened circumference, by a
curve, we form the curve of sines, or the sinusoid.
The sinusoid occurs often during the study of natural
philosophy. We may meet with it again in our book on
the nature of light, and it certainly will occur in our book
on heat.
AN EXPERIMENT WHICH GIVES US THE TRACE OF A
VIBRATING PINE ROD.
A in Fig. 10 represents a rod 4 feet (121.9 centi-
metres) long, 1 inch (25 millimetres) wide, and 4 inch (6
millimetres) thick, made of clear, well-seasoned pine.
This is fastened by means of small screws to the
wooden box # standing on a table. This box may .
be of any convenient size ; but, as it is to be used for
another experiment, it may be made about 14 inches (35.5
centimetres) square and 30 inches (76.2 centimetres)
high. A shoe-box will answer for the purpose. This
42 SOUND.
box is placed on the table, and then filled half full of
sand, and it thus gives us a firm and solid block against
which to fasten the rod. The lower edge of the rod is
placed about 14 inch (88 millimetres) above the table,
Fre. 10.
with about 3 feet (91.4 centimetres) projecting beyond
the box. At the free end is fastened a small camel’s-hair
pencil, with its tip cut off square, When these things are
in place, get a narrow piece of board, C, just thick enough
to touch the tip of the pencil on the rod when the board
is laid on the table under it. Then tack down a strip of
wood, D, parallel with the rod, to serve as a guide for the
board. On the board tack a sheet of white paper. Dip
a pen in thick black ink, and wet the pencil with it. The
paper-covered board is now laid under the rod, with the
pencil just touching it.
EXPERIMENT 9.—Now draw the end of the rod to
one side and let it vibrate. The pencil will make a trace
on the paper which is nearly straight. Make it vibrate
NATURE OF VIBRATORY MOTIONS. 43
again, and then slide the paper-covered board steadily and
quickly to the left, and the pencil will make on the paper
a sinuous trace.
Examine attentively this wavy line. It looks very
much like the curve of sines which the sand-pendulum
traced for us. If it should be exactly like that curve,
what would it show? Surely, nothing less than that the
rod vibrates to and fro with the same kind of motion as has
a swinging pendulum. ‘To test this supposition make the
following experiment :
EXPERIMENT 10.—Obtain a trace of the vibrating pine
rod in which each flexure in the trace is of the same
length. ‘This we will only get when we move the paper
with a uniform velocity under the vibrating rod. Now,
obtain a trace in sand, on another paper-covered board,
drawn under the sand-pendulum. This trace must be .
made by swings of the pendulum which exactly equal the
breadth of the swings made by the vibrating rod. Draw
the board under the sand-pendulum with different ve-
locities, till you succeed in making the waves of the
sand just as long as those made by the vibrating rod.
That is to say, the distances from 1 to 2, or from 5 to 6,
of Fig. 8, must be the same in both traces. Now, with a
pencil, carefully draw a line through the centre of the
curve traced in sand. Remove the papers from their
boards, and place one over the other on a window-pane.
- After a few adjustments, you will see that one curve lies
exactly over the other, showing that they are exactly the
same in form.
Thus you have yourself found out this very impor-
tant truth in science: A vibrating rod swings to and
fro with the same kind of motion as has a swinging
pendulum,
44 SOUND.
THE PENDULAR MOTION REPRODUCED FROM THE TRACES
OF THE PENDULUM AND VIBRATING ROD.
We have seen that the pendulum and vibrating rod
give traces of the curve of sines. We now will show
how, from this curve, we may get again the pendular mo-
tions which traced it.
EXPERIMENT 11.—Get a postal-card and cut in it a
narrow slit »4; inch (1 millimetre) wide, and slightly
longer than the sinusoidal trace of the vibrating rod, or
pendulum. Lay this over the trace, near one end, so that
you can see a small part of the trace through the slit, as
is shown in Fig. 11. Move the card over the trace, in the
direction of the line A B, and you will see the little dot
swing backward and forward in the slit, and exactly re-
_ peating the motions of the pendulum or vibrating rod.
Fig. 11.
We will hereafter see (Chapter VII. and Experiments
58 and 110) that the molecules of air, and of other elastic
bodies, swing to and fro in the line of the direction in
which sonorous vibrations are traveling through them.
In the above experiment (11), this direction is represented
by the direction of the length of the slit ; or, as it is gen-
erally stated, the sound is moving in the direction of the
length of the slit.
ExPERIMENT 12.—Another method of exhibiting this
matter is to take off the pen and fasten, with wax, a lit-
NATURE OF VIBRATORY MOTIONS. AD
tle point of tinsel on the end of the rod, so that it just
touches a piece of smoked glass laid under it. Vibrate
the rod and slide the glass under it, and we shall get a sin-
uous trace on the glass.
To prepare the smoked glass, lay a piece of gum-cam-
phor, about the size of a pea, on a brick. Then bend a
piece of tin into the shape of a funnel, about 2 inches
high, and cut a number of little notches round the bottom.
Set fire to the camphor and place the funnel over it,
and then by moving the glass about in the smoke which
comes from the funnel it will soon be well blackened.
In exhibiting this trace in the lantern, so that several
can see it at once, it is best to keep the card. with the slit
still and move the glass over it, and then the audience will
see on the screen a white spot on a dark ground, moving
with precisely the motion of a pendulum.
BLACKBURN’S DOUBLE PENDULUM.
ExpErrmMEntT 13.—Let us return to our sand-pendulum.
We have examined the vibrations of a single pendulum,
let us now examine the vibrations of a double pendulum,
giving two vibrations at once. The little copper ring 7,
in Fig. 12, on the cord of our pendulum, will slip up and
down, and by moving it in either direction we can combine
two pendulums in one. Slide it one-quarter way up the
cord, and the double cord will be drawn together below
the ring. Now, if we pull the bob to the right or left, we
can make it swing from the copper ring just as if this
point were a new place of support for a new pendulum.
As it swings, you observe that the two cords above the
ring are at rest. But the upper pendulum can also be
made to swing forward and backward, and then we shall
~
46 SOUND.
have two pendulums combined. Let us try this and see
what will be the result.
Just here we shall find it more convenient to use the
metric measure, as it is much more simple and easy to re-
S=S
rT
INTRII i ii mi
\ ST I IM a
|
|
iI
|
|
1
|
1
.
|
|
|
|
|
2
= AA Bx =F =
member than the common measure of feet and inches. If
you have no metric measure you had best buy one, or
make one. Get a wooden rod just 39,31, inches long, and
divide this length into 100 parts. To assist you in this,
you may remember that 1 inch is equal to 25,4, milli-
metres. ‘Ten millimetres make a centimetre, and 100 centi-
metres make a metre.
NATURE OF VIBRATORY MOTIONS. 47
Now slide the ring 7, Fig. 12, up the cords till it is 25
centimetres from the middle of the thickness of the bob.
Then make it exactly 100 centimetres from the under side
of the cross-bar to the middle of the thickness of the bob,
by turning the violin-key on the top of the apparatus.
At D, Fig. 12, is a small post. This post is set up
anywhere on a line drawn from the centre of the plat-
- form, and making an angle of 45° with a line drawn from
one upright to the other. Fasten a bit of thread to
the string on the bob that is nearest to the post, and draw
the bob toward the post and fasten it there. When the
bob is perfectly still, fill the funnel with sand, and then
hold a lighted match under the thread. The thread will
burn, and the bob will start off on its journey. Now, in
place of swinging in a straight line, it follows a curve, and
the sand traces this figure over and over.
Fire. 13.
Here we have a most singular result, and we may
well pause and study it out. You can readily see that we
have here two pendulums. One-quarter of the pendu-
lum swings from the copper ring, and, at the same time,
the whole pendulum swings from the cross-bar. ‘The bob
cannot move in two directions at the same time, so it
makes a compromise and follows a new path that is made
up of the two directions.
3
48 SOUND.
The most important fact that has been discovered in
relation to the movements of vibrating pendulums is that
the times of their vibrations vary as the square roots of
their lengths. ‘The short pendulum below the ring is 25
centimetres long, or one-quarter of the length of the longer
pendulum, and, according to this rule, it moves twice as
fast. The two pendulums swing, one 25 centimetres and
the other 100 centimetres long, yet one really moves twice
as fast as the other. While the long pendulum is making
one vibration the short one makes two. The times of
their vibrations, therefore, stand as 1 is to 2, or, expressed
in another way, 1: 2.
EXPERIMENT 14.—Let us try other proportions and see
what the double pendulum will trace. Suppose we wish
one pendulum to make 2 vibrations while the other makes
3. Still keeping the middle of the bob at 100 centimetres
from the cross-bar, let us see where the ring must be
placed. The square of 2 is 4, and the square of 3 is 9.
Hence the two pendulums of the double pendulum must
Fia. 14.
have lengths as4isto9. But the longer pendulum isalways |
1,000 millimetres. Hence the shorter pendulum will be
found by the proportion 9: 4: : 1,000 : 444.4 millimetres.
Therefore we must slide the ring up the cord till it is
444.4 millimetres above the middle of the thickness of
the bob.
NATURE OF VIBRATORY MOTIONS. AR 49
Mm. Mm.
2 = 1,000: 250.0........ Octave
:8 = 1,000; 444.4........ vo ee Fifth.
:4 = 1,000: 562.5........ : Fourth.
: 5 = 1,000: 640.0........ : Major Third.
:6 = 1,000: 694.4....... i ) Minor Third,
ate as 1.000)8194.6. 5°, aes : Sub-Minor Third.
BS ee LOOU, = 100.0 ns Bec ae | pipe Second.
pO 1,000 2790.1)... aa Second.
50 SOUND.
Fasten the bob to the post as before, fill it with sand,
and burn the thread, and the swinging bob will make this
singular figure (Fig. 14).
EXPERIMENT 15.—F rom these directions you can go
on and try all the simple ratios, such as 3: 4, 4:5, 5: 6,
6:7, 7: 8, and 8:9. In each case raise the two fig-
ures to their squares, then multiply the smaller num-
ber by 1,000, and divide the product by the larger num-
ber ; the quotient will give you the length of the smaller
pendulum in millimetres. Thus the length for rates of
vibration, as 8 is to 4, is found as follows: 3 X 3 =
9,4 xX 4= 16, and 2*1000 —562.5 millimetres.
The table (Fig. 15) gives, in the first and second col-
umns, the rates of vibration, and in the third and fourth
columns the corresponding lengths of the longer and
shorter pendulums. Opposite these lengths are the fig-
ures which these double pendulums trace. In the sixth
column are the names of the musical intervals (see page
49) formed by two notes, which are made by numbers of
sonorous vibrations, bearing to each other the ratios given
in the first and second columns.
FIXING THE CURVES ON GLASS.
ExPERIMENT 16.—These interesting figures, traced in
sand by the double pendulum, may be fixed on glass in a
permanent form ; and, when framed, will make beautiful
ornaments for the window or mantel, and will remind you
that you are becoming an experimenter. Procure squares
of clear glass about’ six inches on the sides, and buy at
the painter’s a small quantity of French varnish, or clear
spirit-varnish. Hold one of these pieces of glass level in
the left hand by one corner, and, with the right, pour
NATURE OF VIBRATORY MOTIONS. 51
some of the varnish upon the glass. Let the varnish
cover half the glass, and then gently tip the glass from
side to side till the varnish runs into every corner ; then
tip it up, and rest one corner in the mouth of the varnish-
bottle, and rock the glass slowly from side to side. This
will give a fine, smooth coat of varnish to the glass, and
we may put it away to dry. When-the varnish is hard,
lay the glass, varnished side up, on the stand, adjust the
pendulum to make one of the figures, and then fasten it
to the post. Burn the thread, and stop the motion of the
bob as soon as the figure is finished. Brush away any
extra sand that may lie at the ends of the figure, and
then take the glass carefully to a hot stove. Have some
wooden blocks laid on the stove, and rest the glass on
these. Presently the varnish will begin to melt, and then
the glass may be lifted and carefully put away to cool,
taking the utmost care not to disturb the sand. When
the varnish is hard, the sand which has not stuck is re-
moved by gently rapping the edge of the plate on the
table. Then we shall have a permanent figure of the
curve. To preserve it, lay small pieces of cardboard at
each corner and narrow strips half-way along the edges,
and then lay another piece of glass over these, and bind
the two together with paper on the edges. The plate
may now be placed on the lantern, and greatly magnified
images of the curves may be obtained on the screen.
EXPERIMENTS IN WHICH WE COMBINE THE MOTIONS OF
TWO VIBRATING RODS.
We have just seen how the double pendulum combines
into one movement the motions of two pendulums swing-
ing at right angles to each other. Our experiments have
LIBRARY
UNIVERSITY OF ILLINOIS
52 —
also taught us that the numerical relation between the
numbers of swings of the two pendulums is shown by
the curved figure produced ; so that, knowing the figure,
we can tell the relative number of vibrations of each
pendulum, and, from knowing the latter, we can pre-
x |
e
aa
————————
f es
dict the curved figure that the double pendulum will
draw. But our experiments have taught us that a vibrat-
ing rod moves to and fro with the same kind of motion as
a swinging pendulum. From this it follows that, if by
any means we can combine into one motion the separate
NATURE OF VIBRATORY MOTIONS. 53
motions of two vibrating rods, we shall make these rods
describe the curved figures traced by the double pendulum.
The motions of two vibrating rods may be combined
into one motion by means of a beam of light, which, fall-
ing on a mirror fastened to the end of one rod, is reflected
to a mirror fastened to the end of the other rod, while
from this second mirror the beam is reflected to a screen.
It is absolutely necessary for the success of these ex-
periments that the vibrating rods should be fastened to
bodies which are heavy and firm, and do not vibrate when
the rods are set in motion. Boxes A and B of Fig. 16,
about 14 inches square, half filled with sand, gravel, or
dry earth, make such supports. The rods Cand D are of
clear, white pine, 4 feet (121.9 centimetres) long, 1 inch
(25 millimetres) wide, and 4 inch (6.25 millimetres)-thick.
On the end of each rod is fastened with wax a silvered
glass mirror, 1 inch square. The upright rod C is fast-
ened to the side of the box A by two screws, which go
through the rod and into the box near the edge of its top.
Another screw fastens the rod to the box at a distance of
several inches below the upper screws. 'The free end of
this rod, above the box, is exactly 30 inches (76.2 centi-
metres). The length of the horizontal rod D can be
changed at will, for it is clamped to the side of the box
B by screws, which go through the ends of the two
pieces of wood /’ and G. Two nails are driven into the
box under this rod, and serve to guide it in a horizontal
direction while we slide it out-or in. i.
TRANSMISSION OF SONOROUS VIBRATIONS. VE
this is so you may prove for yourself by the following
experiment :
Exprrmment 44,—Being careful not to move the glass
plate from its present position (Experiment 43), stick it
with wax to the tumbler. Pour a little silica into the
tumbler, and then hold it horizontally, and vibrate the
fork near its opening, observing attentively how the silica
powder is acted on by the inclosed vibrating air.
EXPERIMENT 45.—Take a piece of thin linen paper
about 44 inches square, and having wetted it paste it over
the mouth of the tumbler. When the paper_has dried it
will be stretched tightly...Take a sharp penknife and
carefully cut away the paper so as to make an opening as
shown at B in Fig. 27. Make this opening small at first,
and very gradually make it larger and larger. Hold the
fork over the opening after each increase in its size, and
you will soon discover the size of the opening which
causes the air inclosed in the tumbler to vibrate with the
fork, and thus greatly to strengthen its sound. You have
now a mass of air in tune with the fork, and inclosed in a
vessel which has one of its walls formed of a piece of
elastic paper. With this instrument, which I have invented
for you, you must make some charming experiments.
Exrrrtment 46.—If the air in the tumbler vibrates to
the A-fork, it will, of course, vibrate to the A-pipe, which
gives the same note as the fork. Scatter some sand on
the paper, and then sound the A-pipe a foot or two from
it. The sand dances vigorously about, and ends by
arranging itself in a nodal line parallel to the edges of
the paper, in the form of a U with its two horns united
by a straight line. The vibrations of the pipe can only
reach the tumbler by going through the air, and, as the
sand vibrates when the tumbler is placed in any position
"8 SOUND
about the pipe, it follows that the air all around the pipe
vibrates while the pipe is sounding.
ExpERIMENT 47.—Sprinkle a small quantity of sand
on the paper, and then, placing a thin book under the tum-
bler, so incline it that the sand just does not run down the
paper, as shown in B, Fig. 27. Now go to the farthest
end of the room and blow the pipe in gentle toots, each
about one second long. At each toot, your friend, stand-
ing near the tumbler, will see the sand make a short march
down the paper; and soon by a series of marches it makes
its way to the edge of the paper and falls into the tum-
bler. I have, in a large room, gone to the distance of
60 feet (18.28 metres), and the experiment worked as I have
just described it.
ExPERIMENT 48.—Again arrange the experiment as in
Experiment 47, and standing 3 or 4 feet from the tumbler
try how feeble a sound will vibrate the paper. If every
part of the experiment is in good adjustment, you will find
that the feeblest toot you can make will set the sand
marching. To keep it at rest you must keep silent.
ExpPERIMENT 49.—To show these experiments on a
greatly magnified scale, place the tumbler in front of the
heliostat (sce “Light,” page 79) so that the sun’s rays just
graze along the inclined surface of the paper. Cut off a
piece of a match 4 inch long, and split this little bit mto
four parts. Place one of these on the inclined paper. Of
course, the image of the tumbler is inverted, so the bit of
wood appears to adhere to the lower side of the paper.
If a little paper mouse cut out of smooth paper is used in
place of the bit of wood, it is really amusing to see the
mouse make a start to every toot of the pipe. I trust
my reader will not think me unscientific for making a
little fun. Singing the note A, instead of sounding it
TRANSMISSION OF SONOROUS VIBRATIONS. 19%
on the pipe, produces the same effects in the above ex-
periments.
EXPERIMENT 50.—If you sing or sound some other
note than the A, you will find it powerless to move the
sand over the tumbler.
EXPERIMENT 51.—The experiments just made with the
tumbler, partly covered with the glass plate or stretched
paper, may be modified in a way that makes one of the
most beautiful and instructive experiments.
Take a pint bottle half filled with distilled or rain
water, and put into it one ounce of shavings of white cas-
tile soap ; then shake the bottle. If the soap does not all
dissolve, add more water till you have a clear solution.
_ Then add a gill of glycerine, shake, and allow to settle.
This solution is the best for making soap-bubbles.
Pour out the soap-solution into a basin; then dip the
mouth of a deep tumbler (one 5 or 6 inches deep is the best)
into it. The glass plate is now slid through the soap-
water under the mouth of the tumbler. Take the tum-
bler, with the glass on it, out of the basin and stand it
erect on the table. Vibrate the A-fork, and hold it over
the edge of the tumbler while you slide the glass plate
across its mouth, as we did in our other experiments.
‘The opening which is thus made, between the rim of the
tumbler and the edge of the glass plate, will have a soap- -
film over it. Adjust the size of this opening till it tunes
the air in the tumbler to vibrate to the fork. When this
takes place, a loud sound issues from the tumbler, and the
delicate soap-bubble is violently agitated ; its surface is
chased and crinkled in so complicated a manner that its
appearance cannot be described.
This experiment succeeds best with a very deep tum-
bler, like the one we have used, and with a C-fork and
80 SOUND.
pipe. The soap-film covers nearly half of the mouth of
the tumbler when the latter is in tune to the O-fork.
To see well the vibrating surface of soap-film, you
must reflect from it the light of the sky.
EXPERIMENT 52.—By the aid of the heliostat and a
lens the experiment may be made one of. great beauty.
With some wax stick the glass plate to the tumbler, so
that the soap-film may be placed upright and inclined to
the beam of light coming from the heliostat. With a plano-
convex lens placed between the film and the screen obtain
a magnified image of the soap-film (see “ Light,” page 79).
As the soap-film is upright it drains thinner and thin-
ner, While the image of the film grows more and more
brilliant. Magnificent bands of reddish and bluish light
appear, and stretch across the screen. Now sound the
fork or pipe near the film. The vibrations bend and un-
dulate the colored bands, and the colors chase each other
over the screen like waves on a troubled sea. On the
sound ceasing, the bands straighten, and a comparative
calm spreads over the screen.
EXPERIMENTS WITH THE SENSITIVE-FLAMES OF GOVI
AND BARRY, AND OF GEYER.
EXPERIMENT 53.—In Fig. 28, A is an upright wooden
rod nailed to a block D. At B is a piece of stout wire
bent in the form of a ring, 5 inches (12.7 centimetres) in
diameter, and then bent at a right angle and stuck in the
upright rod. On the ring is laid a piece of wire gauze
that has about 30 meshes to the inch. /# is a glass tube
joined to a rubber tube that leads to the nearest gas-
burner. To make this glass tube or jet, take a piece of
glass tube, about + inch outside diameter and: 6 inches
TRANSMISSION OF SONOROUS VIBRATIONS. 81
(15.2 centimetres) long, and, holding its ends in the hands,
heat the tube, at about 14 inch from its end, in a spirit-
flame or the flame of a Bunsen burner till it softens ;
then pull it out till it is reduced about one-quarter in di-
ameter. When it is cold, draw the edge of a file across
this narrow part, and snap the tube asunder. Now heat
in like manner the middle of this tube, and bend it into a
right angle, as shown in Fig. 28, and, with wax, stick it
upright on a block of wood, with the tip of the jet about
2 inches (5.1 centimetres) below the wire gauze.
Turn on the gas and light it above the gauze, where
it will burn in a slender, conical flame, about 4 inches
high, with its top yellow and its base blue. This forms
the “sensitive-flame” invented by Prof. Govi of Turin,
and afterward by Mr. Barry of Ireland.
82 SOUND.
If you hiss, whistle, shake a bunch of keys, or clap
the hands, the flame at once roars, and, shrinking down
to the gauze, becomes entirely blue and almost invisible.
It is called a ‘“ sensitive-flame,” because it is sensitive
to sonorous vibrations, and shows us their existence in
the air.
Exprrtment 54,—Mr. Geyer, of the Stevens Institute
of Technology, has made an addition to the Govi-Barry
flame, which heightens its sensitiveness, and makes it
utter a musical note while disturbed by vibrations ;
while, in another modification of the experiment, the
flame sings continuously, except when agitated by exter-
nal sounds. I give his experiments in his own words :
‘“‘ To produce them it is only necessary to cover Barry’s flame
with a moderately large tube [see Fig. 28, in which, however, the
tube is represented of somewhat too great a diameter], resting it
loosely on the gauze. A luminous flame, 6 or 8 inches long, is
thus obtained, which is very sensitive to high and sharp sounds.
If, now, the gauze and tube be raised, the flame gradually shortens,
and appears less luminous, until at last it becomes violently agi-
tated, and sings with a loud, untform tone, which may be main-
tained for any length of time. Under these conditions, external
sounds have no effect upon it. The sensitive musical flame is
produced by lowering the gauze until the singing just ceases. It
is in this position that the flame is most remarkable. At the
slightest sharp sound, it instantly sings, continuing to do so as
long as the disturbing cause exists, but stopping at once with it.
So quick are the responses that, by rapping the time of a tune,
or whistling or playing it, provided the tones are high enough,
the flame faithfully sounds at every note. By slightly raising or
lowering the jet, the flame can be made more or less sensitive, so
that a hiss in any part of the room, the rattling of keys even in
the pocket, turning on the water at the hydrant, folding up a
piece of paper, or even moving the hand over the table, will excite
TRANSMISSION OF SONOROUS VIBRATIONS. 83
the sound. On pronouncing the word ‘sensitive,’ it sings twice;
and, in general, it will interrupt the speaker at almost every ‘s,’
or other hissing sound.
‘‘The tube chiefly determines the pitch of the note, shorter or
longer ones producing, of course, higher or lower tones respec-
tively. I have most frequently used either a glass tube, 12 inches
long and 1} inch in diameter, or a brass one of the same dimen-
sions. Out of several rough pieces of gas-pipe, no one failed to
give a more or less agreeable sound. Among these gas-pipes was
one as short as 7 inches, with a diameter of 1 inch; while an-
other was 2 feet long and 14 inch in diameter.:: A third gas-pipe,
15 inches long and # inch in diameter, gave, when set for a con-
tinuous sound, quite a low and mellow tone.
“If the jet be moved slightly aside, so that the flame just
grazes the side of the tube, a note somewhat lower than the fun-
damental one of the tube is produced. This sound is stopped by
external noises, but goes on again when left undisturbed. All
these experiments can be made under the ordinary pressure of
street-gas, # inch of water being sufficient.”
84 SOUND.
’ CHAPTER VII.
ON THH VELOCITY OF TRANSMISSION OF SONOROUS
VIBRATIONS, AND ON THE MANNER IN WHICH THEY
AkE PROPAGATED THROUGH ELASTIC BODIES.
/
ON THE SPEED WITH WHICH SONOROUS VIBRATIONS
TRAVEL.
WHEN in the country, you have seen a man chopping
wood. If you stood near him, you observed that the
blow and the sound of his ax came together. If you
moved. away from him, you may have noticed that, while
you could see his ax fall, and hear the sound of the blow,
the sound seemed to follow the blow. When you moved
away several hundred feet, the interval of time separating
the sight of the blow and its sound was readily noted.
You may also have observed that some time passed be-
tween the flash of a gun or the puff of a steam-whistle
and the report of the gun and the sound of the whistle.
These things convince us that sonorous vibrations take
time to move through the air.
This matter has been carefully examined by scientific
men, and they have found that sound-vibrations move
through the air at the rate of 1,090 feet (332.23 metres)
in one second. This is the velocity of sound when the
temperature is just at freezing, or at 32° Fahrenheit. For
each degree above this, sound gains in speed one foot more.
VELOCITY OF TRANSMISSION, ETC. 85
For instance, upon a summer’s day, the thermometer may
stand at 80°. This is 48° above 32°, and the sound gains
48 feet, so that it moves at the rate of 1,138 feet a second
at this temperature. |
The velocity of sonorous vibrations in oxygen gas at
32° is 1,040 feet per second ; in hydrogen gas it is 4,160
feet, just 4 times as great. Asa cubic foot of hydrogen
weighs 16 times less than a cubic foot of oxygen, and as
4 is the square root of 16, it follows that the speed of
sonorous vibrations in gases varies inversely as the square
roots of the weights of equal volumes of the gases.
Sonorous vibrations travel through water at the speed
of 5,000 feet per second, and through iron at about 16,000
feet in a second.
EXPERIMENTS WITH GLASS BALLS ON A CURVED RAILWAY,
SHOWING HOW VIBRATIONS TRAVEL THROUGH ELASTIC
BODIES.
Experiment 55.—Fig. 29 represents a wooden rail-
way about 6 feet (183 centimetres) long. It may be
made of pine strips, 14 inch (3.8 centimetres) wide and 4
inch (6 millimetres) thick, laid side by side about 1 inch
Fig, 29.
(25 millimetres) apart, and joined together by short cross-
strips nailed on them. Get six or seven large glass mar-
bles at the toy-shop. These are intended to roll be-
86 SOUND.
tween the two strips, just as balls roll in the railway of a
bowling-alley. Place the railway on a table or board,
and fasten it down at the middle with a screw in the
cross-strip, and then raise each end and put a book or
wooden block under it, as in Fig. 29.
Place the balls in the middle of the curving railway,
and then bring one to the end and let it roll down against
the others. Immediately the last ball will fly out and roll
part way up the incline toward the other end of the rail-
7 ee
Fig. 82.
way. The first ball will come to rest beside the others,
and the ball which has been shot up the railway will roll
back against those at rest, and the same performance will
be repeated till the motion has gone from the rolling balls.
Let us examine this matter, and see what happens
to these balls on the railway. First, you must observe
that the balls are elastic, for experiment will show that
they will bound like rubber balls when let fall on the
hearth-stone.
ExPERIMENT 56.—To show that the ball is elastic, and
jfiattens when it strikes the stone, make the following ex-
periment: Mix some oil with a little red-lead, or other
colored powder, and smear it over a flat stone, like a flag-
VELOCITY OF TRANSMISSION, ETC. 87
stone. Rest the ball on this, and observe the size of the
circular spot made on it. Now let the ball fall on the
stone, and observe the larger circular spot_made by the
fall. This shows that when the ball struck it flattened
and touched a larger. surface.on the.stone..
The first ball rolls down and strikes a hard blow on
the side of ball No. 2. This ball is flattened between
balls Nos. 1 and 3, as shown in Fig. 30.
Ball No. 2 at once springs back again into its former
spherical figure, and in doing so it brings No. 1 to rest
and flattens No. 3, as shown in Fig. 31.
Ball No. 3 now springs back into its spherical form,
and in doing so acts on No. 2 and brings it to rest, and
acts on No. 4 and flattens it. Thus each ball passes the
blow on to the next by its elasticity, and each in turn
flattens and then springs into its natural form, and thus
we have a series of contractions and expansions running
through the whole series of balls. The last ball is finally
flattened, and, when it expands immediately afterward, it
presses against the ball that gave it the blow and brings
it to rest; at the same time, finding no resistance in
front of it, its back-action on the ball behind it causes it
to start up the railway. Thus the last ball, No 7, is shot
up the railway by a force derived from ball No. 1, and
which was sent through all the balls by their successive
contractions and expansions. |
EXPERIMENTS WITH A LONG SPRING, SHOWING HOW VI-
BRATIONS ARE TRANSMITTED AND REFLECTED.
ExPERIMENT 57.—Obtain a brass wire, wound in the
form of a spiral spring, about 12 feet long. Get an
empty starch-box or cigar-box, and take off the cover,
and then stand it on one end at the edge of a wooden
88 SOUND.
table, with the bottom of the box facing outward. Screw
this box firmly to the table, and then screw a small iron
or brass hook to the bottom of the box, as shown in Fig.
33. Slip over this hook the loop at the end of the long
spiral spring. Hold the other end of the spring in the
hand, letting it hang loosely between the hand andthe
box. Insert a finger-nail or the blade of a knife between
the turns of the wire, near the hand, and pull the turns
Fre. 33.
asunder. Free the nail suddenly, and a vibration or
shock will start and run from coil to coil along the whole
spring, and a loud rap or blow will be heard on the box,
thence to be reflected to the hand, and then again to the
box, and so on. Here we have a beautiful illustration of
the manner in which a vibration may travel along an elas-
tic substance, and make itself heard as a sound at the
VELOCITY OF TRANSMISSION, ETC. 89
other end, there to be reflected back to the place whence
it came, to begin over again its forward journey.
EXPLANATION OF THE MANNER IN WHICH SONOROUS
VIBRATIONS ARE PROPAGATED.
If the student clearly understands the actions in the
experiments with the glass balls and spring-coil, he can
have no difficulty in perceiving how a shock or vibration
may in like manner pass through the elastic air.
For simplicity of illustration, imagine a very long
tube, in which, at one end, fits a piston or plug. ‘Suppose
this piston moves quickly forward in the tube through a
short distance—say, one inch—and then stops. If the air
were inelastic, then one inch of air would move out of the
other end of the tube while the piston moved forward one
inch. But air is elastic ; it gives before the motion of the
piston ; and it takes some time, after the piston has moved
forward, before the air moves at the other end of the tube.
If the tube is 1,100 feet long, and the temperature of the
air 42°, it will be one whole second before the end of the
air-column moves ; for it takes that.time for a sound-vi-
bration to traverse 1,100 feet, and a mechanical action on
air of the above temperature cannot be sent through it
with a greater speed than that.
Now, suppose that the piston takes 4, second to make
its forward motion in the tube, how far will the air be
compressed in front of it at the instant the piston stops ?
Evidently the answer is found by taking +, of 1,100 feet,
which is 110 feet. If the piston takes ;4, of a second in
moving forward, then at the end of that time the air is
compressed before the piston to a depth of 7}, of 1,100
feet, or 11 feet. The length of the column of air, com-
pressed by the forward motion of the piston, in every case
90 SOUND.
is found by dividing the velocity of sound by the fraction
of a second during which the piston was moving.
This compressed air cannot remain at rest in the tube,
for it is now exactly like the compressed ball “No. 2, of
Fig. 30. It expands, and in expanding it acts backward
against the immovable piston, but in front it compresses
another column of air equal to it in length ; this, in turn,
acts like ball No. 3 of Fig. 31, bringing to rest the column
of air behind it and compressing another column in front
of it ; and in this manner the compression will traverse a
tube 1,100 feet long in one second.
If the piston moves backward in the tube, then a col-
umn of rarefied or expanded air will be formed in front of
the piston, caused by the air expanding into the space left
vacant by its backward motion ; and this rarefaction will go
forward through the air exactly as did the compression.
Now imagine the piston to move to and fro in the
tube ; it will send through the column of air condensa-
tions and rarefactions, following each other in regular
order. If we have a body vibrating freely in the open
air, then it will form spherical shells of compressed and
rarefied air all around it, these shells constantly expand-
ing outward into larger and larger shells, and following
each other in regular order and motion, like the regular
movement of the circular water-waves which spread out-
ward around a point of agitation on the surface of a pond.
Thus the sound-vibrations are sent out in all directions
from a vibrating body just as light is diffused in all direc-
tions around a luminous body. In our experiments in
“Tight,” page 34, we found that the illumination of a
given surface varies in brightness inversely as the square
of its distance from the source of light. In like manner
the loudness of a sound decreases inversely as the square
~
VELOCITY OF TRANSMISSION, ETC. 91
of our distance from the vibrating body. Thus, at 100
feet, the loudness of the sound is + of what it was at 50
feet, and at 200 feet its loudness is = of what it was
when we were 50 feet distant.
Now what will be the effect on any TO of air—
like that, for example, which touches the drum-skin of the
ear—if these condensations and rarefactions reach it?
Evidently, while the condensations are passing, the mole-
cules (the smallest parts) of the air will move nearer each
other, then regain their natural positions, to be separated
yet farther by the rarefaction which at. once follows.
Therefore, the effect on any molecule will be to swing it
to and fro. Hence the air, touching the drum-skin of the
ear, moves forward and then backward, and forces the
drum-skin in and then out. This swinging motion is con-
veyed to the fibres of the auditory nerve, and causes that
sensation called sound.
But we have seen that vibrating bodies swing to and
fro like the pendulum, hence those vibrating bodies which
are causing sound make all the molecules of air around
them swing to and fro like the bobs of very small pendu-
_ lums, each pendulum beginning its swing just a little
sooner than the one in front of it.
All this, however, and much more than we have time
to write about, will be taught you very clearly by an in-
strument which I shall now show you how to make.
~ EXPERIMENTS WITH CROVA’S DISK, SHOWING HOW SONO-
ROUS VIBRATIONS TRAVEL THROUGH AIR AND OTHER
ELASTIC MATTER.
ExrERIMENT 58.—In Fig. 34 A is a cardboard disk
mounted on a whirling machine or rotator B, and C is a
92 7 SOUND.
one
for
a { fae
; " yu
HN mee i
AIAN APA A
piece of cardboard having a slit cut in it. Upon the disk
are 24 eccentric circles drawn with a pen, and so placed
that they can be seen through the slit in the cardboard.
VELOCITY OF TRANSMISSION, ETC. 93
The rotator can be bought of Mr. Hawkridge of Hoboken
for $3.00 ; the disk you can make yourself from the fol-
lowing directions : Get a piece of stiff cardboard, and cut
out a disk 31 centimetres in diameter. In making this
disk we will use the metric measure exclusively. Round
the centre C’ of this disk draw a circle just 5 millimetres
in diameter. (See C, Fig. 35, where it is drawn “full
size.”) Then divide this circle into 12 parts, and number
the points of division 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12.
The next step is to rule upon a sheet of paper a straight .
line 143 centimetres long, and to mark 72 millimetres of
this off into 24 spaces of 3 millimetres each, as shown in
the real size at A B, Fig. 35. This we use as a scale in
spreading the dividers. Then draw a circle with the di-
viders spread 74 centimetres, from A to B, Fig. 35, using
the dot No. 1 at the top of the circle C on the cardboard
as acentre. Then spread the compasses just 3 millimetres
wider, using the scale we have just made for a guide, and
make another circle, with dot No. 2 as a centre. You will
observe that the two circles are eccentric—that is, they
are not parallel to each other, one spreading a little to the
right of the other. Go thus round the circle C twice, and
use each dot in the circle in turn as a centre till you have
24 eccentric circles drawn on the disk, each circle having
a radius 3 millimetres greater than the one next within it.
When the circles are finished, ink them over with a draw-
ing-pen holding violet ink, or Indian-ink. When dry, cut
a small hole exactly in the centre, and mount the disk on
the rotator. Get a piece of cardboard about 15 centi-
metres long, and cut in it a narrow slit about 10 centi-
metres long, in which the eccentric circles will appear
like a row of dots when the cardboard is held before the
disk, as in Fig. 34.
SOUND.
CROVAS DISK,
Yop, SIZE.
Fra. 85.
VELOCITY OF TRANSMISSION, ETC. 95
- Now turn the handle of the rotator slowly and steadily.
The disk will revolve, and the eccentric circles will move
in the slit in the card. At once you have a most singular
appearance. A horizontal, worm-like movement among
the row of dots is seen in the slit. They crowd up
against each other and then move apart, only to draw
near again and then separate. ‘There seems to be a wave
moving along the slit, appearing at one end and disappear-
ing at the other. At one part of the wave the dots are
crowding together, at another they are spreading apart.
Look closely and you will observe that, although this
wave appears to move over the length of the slit, yet each
dot makes but a very small to-and-fro movement. No
matter how fast the crank is turned, or how swiftly the
waves chase each other along the slit, each dot keeps
within a fixed limit, swinging to and fro as the waves pass.
We have learned that the prongs of a tuning-fork vi-
brate like a pendulum. Both prongs move, but just now
we will only consider the motion of one. In vibrating it
swings backward and forward, pushes the air in front of
it, and gives it a squeeze ; then it swings back and pulls
the air after it. In this way the air in front of it is alter-
nately pressed and pulled, and the molecules of air next
_ to it dance to and fro precisely as the first dot swings to
and fro behind the slit. You cannot see the motion of
the molecules of air in front of the tuning-fork, yet our
apparatus accurately represents their movements so that
we can leisurely study them.
First comes an outward swing of the fork, and the air
before it is squeezed or condensed. Then it swings back,
and the air before it is pulled apart or spread out ; in
other words, it is rarefied. So it happens that the fork
alternately condenses and rarefies the air. The air is elas-
5 .
96 _ SOUND.
tic, and the layer nearest the fork presses and pulls its
neighbors precisely as described in the previous section,
where we explained the manner in which sonorous vibra-
tions are propagated.
When the fork makes one condensation and one rare-
faction, it has made one vibration; that is, it has swung
once to and fro. ‘Then it makes another vibration, and
produces another condensation and rarefaction. Thus
condensations and rarefactions follow each other, and
move away from the fork in pairs, in regular order.
One condensation, together with its fellow rarefaction,
forms what is called a sonorous wave. If the fork, for
example, should vibrate for exactly one second, and then
stop, the air, for a distance of 1,100 feet all around it,
will be filled with shells of condensed and rarefied air.
Therefore, as one vibration to and fro of the fork makes
one shell of condensed air and its neighboring shell of
rarefied air, we can find the combined thickness of these
two shells by dividing 1,100 feet (the velocity of sound)
by the number of vibrations the fork makes in one second.
Our A-fork makes 440 vibrations in one second. Hence
the depth of two shells—one of condensed, the other of
rarefied air—formed by this fork is 1,100 + 440, which is
24 feet. The length thus obtained is called a wave-length.
Evidently, the greater the number of vibrations a second
the shorter the waves produced.
Scientific men, to represent a sonorous wave, always
use a curve like A C O & B of Fig. 36, in which the part
of the curve A C O, above the line A B, stands for the
condensed half of the. wave, while the part O & B, below
A B, stands for the rarefied half of the wave, and the per-
pendicular height of any part of the curve A C O, above
the line A B, shows the amount of condensation of the air
VELOCITY OF TRANSMISSION, ETC. 97
at that part of the wave ; while similar lines drawn to the
curve OF B, below A B, show the amount of rarefac-
tion at these points of the wave.
The curve A C O & Bis not a real picture of a sono-
rous wave ; it is merely a good way of showing its length,
and the manner in which the air is condensed and rare-
fied in it; for sonorous waves are not formed of heaps
and hollows like the waves you have seen on the sea.
They are not heaps and hollows of air, but only conden-
sations and rarefactions of air. In short, Fig. 36 is merely
a convenient symbol which stands for a sonorous wave.
C
ss
R
Fra, 36.
ExpPrERIMENT 59.—Look at the row of dots seen in the
slit when the disk is at rest, and find the two dots which are
- nearest to each other ; this place in the slit corresponds
to the point Cin Fig. 36. Next find where the dots are
farthest apart ; this place corresponds to #& in Fig. 36.
The distance from C to # is one half wave-length ; there-
fore the distance between two adjoining places, where the
dots are nearest together, equals the length of one whole
wave.
98 SOUND.
CHAPTER VIII.
ON THE INTERFERENCE OF SONOROUS VIBRATIONS
AND ON THE BEATS OF SOUND.
ExPERIMENT 60.—Cut out two small triangles of cop-
per foil or tinsel, of the same size, and with wax fasten one
on the end of each of the prongs of a tuning-fork. Put
the fork in the wooden block and set up the guide (as in
experiment, Fig. 21). Prepare a strip of smoked glass,
and then make the fork vibrate and slide the glass under
it, and get two traces, one from each prong.
YING NY MS WADDLE LRP RIRLOS PI IOP II NL LOL LOGS
INS SF NL NIRS OIE L\IV\I.\ LVI IVIL II SV\IVFINW PINS NS
Fig. 387.
Holding the glass up to the light you will see the
double trace, as shown in Fig. 37. You observe that the
wavy lines move apart and then draw together. This
shows us that the two prongs, in vibrating, do not move
in the same direction at the same time, but-always in op-_
posite directions. They swing toward each other, then
away from each other.
ExpERIMENT 61.—What is the effect of this movement
of the prongs of the fork on the air? A ame experi-
ment will answer this question.
INTERFERENCE OF SONOROUS VIBRATIONS. 99
Place three lighted candles on the table at A, B, and
C (Fig. 38). Hold the hands upright, with the space
between the palms opposite A, while the backs of the
hands face the candles Band C. Now move the hands
near each other, then separate them, and make these mo-
tions steadily and not too quickly. You thus repeat the
motions of the prongs of the fork. While vibrating the
hands observe attentively the flames of the candles. When
the hands are coming nearer each other, the air is forced
out from between them, and a puff of air is driven against
the flame A, as is shown by its bending away from the
hands. But, during the above movement, the backs of the
hands have drawn the flames toward them, as shown in
Fig. 838. When the hands are separating, the air rushes
- in between them, and the flame A is drawn toward the
hands by this motion of the air, while at the same time
the flames at B and C are driven away from the backs of
the hands. From this experiment it is seen that the space
100 SOUND.
between the prongs and the faces_of the prongs of a fork
are, at the same-instant, always acting oppositely on the air,
This will be made clearer* by the study of the dia-
gram, Fig. 39.
This figure supposes the student looking down on the
tops of the prongs of the fork. Imagine the prongs
swinging away from each other in their vibration. Then
the action of the faces ¢ and ¢ on the air is to condense it,
and this condensation tends to spread all around the fork.
But, by the same movement, the space 7 7 between the
prongs is enlarged, and hence a rarefaction is made there.
This rarefaction also spreads all around the fork. But,
as the condensations produced at ¢ and ¢ and the rarefac-
tions at 7 and 7 spread with the same velocity, it follows
INTERFERENCE OF SONOROUS VIBRATIONS. 101
that they must meet along the dotted lines qg, q, q, 4,
drawn from the edges of the fork outward. The full
#-circle lines around the fork in Fig. 39 represent the
middle of the condensed shells of air, while the broken
4-circle lines stand for the middle of the rarefied shells
of air.
Now what must happen along these dotted lines, or,
rather, surfaces? Evidently there is a struggle here
between the condensations and the rarefactions. The
former tend to make the molecules of air go nearer
together, the latter try to separate them; but, as these
actions are equal, and as the air is pulled in opposite
directions at the same time, it remains at rest—does not
vibrate. ‘Therefore, along the surfaces q, 4g, q, g, there is
silence. When the prongs vibrate toward each other they
make the reverse actions on the air ; that is, rarefactions
are now sent out from cand c, while condensations are
sent from 7 and 7, but the same effect of silence along
hs % 7 18 produced.
EXPERIMENT 62,—That this is so, is readily proved by
the following simple experiment. . Vibrate the fork and
hold it upright near the ear. Now slowly turn it round.
During one revolution of the fork on its foot, you will
perceive that the sound goes through four changes. Four
times it was loud, and four times it was almost if not
quite gone. Twirl the fork before the ear of a compan-
ion; he will tell you when it makes the loudest sound,
and when it becomes silent. You will find that when it
is loudest the faces ¢, c of the prongs, or the spaces 7, 7
between them, are facing his ear; and when he tells
you that there is silence you will find that the edges
of the fork, that is, the planes qg, 9, g, ¢g, are toward
his ear.
102 SOUND.
AN EXPERIMENT IN WHICH INTERFERENCE OF SOUND IS
SHOWN BY ROTATING A VIBRATING FORK OVER THE
MOUTH OF A BOTTLE RESOUNDING TO THE NOTE OF
THE FORK.
EXPERIMENT 63.—Get a bottle, like one of those shown
in Fig. 40, holding about 5 fluid ounces when filled to its
brim. Its mouth should measure 1 inch (25 millimetres)
in diameter. Cut a piece of glass 1} inch long and 1 inch
wide, and slide this over the mouth of the bottle while
the vibrating A-fork is held over it. Fix the piece of
glass with wax at the place where it makes the air in the
bottle resound the loudest (see Fig. 40).
Again vibrate the fork, and holding it horizontally
twirl it slowly over the partly closed bottle, just as we
twirled it before the ear. You will find that whenever
the corners of the fork have come opposite the mouth of
the bottle the sound will have faded away to silence. In
this position of the fork, one of the planes q, q, ¢g, or q, of
Fig. 39, goes directly down to the mouth of the bottle,
and therefore there enter the bottle, side by side, at the
same time, a condensation and a rarefaction. Hence the
air in the bottle is acted on by two equal and opposed ac-
tions ; it cannot vibrate to the fork, and we have rest
and silence. The above experiment, and the following
one, may be made as well with the tuned tumblers of
Experiment 43 as with the bottles.
“ EXPERIMENTS IN WHICH INTERFERENCE OF SOUND IS OB-
TAINED WITH A FORK AND TWO BOTTLES.
EXPERIMENT 64,—Fig. 40 represents two glass bottles,
of equal size, and each tuned as described in Experiment
INTERFERENCE OF SONOROUS VIBRATIONS. 103
63. Set one bottle upright, and with two bits of wax
hold the other horizontally on some books, with the mouths
of the bottles nearly touching, as shown in Fig. 40.
Make the fork vibrate, and, holding it horizontally,
bring it down so that the space between the prongs will
be opposite the mouth of the upright bottle, as shown in
Fie. 40.
Fig. 40. As it descends, you will observe that the sound
first increases, and then suddenly fades away or entirely
- disappears. You can raise the fork and hear it still sound-
ing, so that you may be sure it has not stopped, and yet,
in a certain position between the two bottles, the sound is
nearly if not wholly lost.
104 SOUND.
In this experiment, you will observe that while the face
of one of the prongs is opposite the mouth of one bottle
the space between the prongs is opposite the mouth of the
other bottle. Therefore, while one bottle receives a con-
densation the other receives a rarefaction. Thus opposed
vibratory motions issue from the mouths of the bottles,
and they neutralize each other’s action on the outside air.
Hence silence is observed when the fork is in such posi-
tion that the condensation or rarefaction which comes out
of one bottle exactly equals in power the rarefaction or
condensation which comes out of the other bottle.
You know that the air is really resounding in the bot-
tles, even when silence is outside of them, by the fol
ing simple experiments :
EXPERIMENT 65.—Slip a piece of cardboard over the
mouth of one of the bottles, and at once the other bottle
resounds to the fork and sings out loudly. The balance
is thus broken and sound is heard.
EXPERIMENT 66.—A piece of tissue-paper will pro-
duce another effect, because it is thin and only partly cuts
off the vibrations, and the result is a feeble sound ; partly
an interference and partly a free action of the condensa-
tions and rarefactions, half silence, half sound.
EXPERIMENT SHOWING REFLECTION OF SOUND FROM A
FLAT GAS-FLAME,
EXPERIMENT 67.—By a little care you can even slide
the flat flame of a fish-tail gas-jet before the mouth of the
horizontal bottle, and thus make a flame act as a guard to
stop the vibrations from entering the bottle.
When two sonorous vibrations meet and make silence,
they are said to “interfere.” ‘The experiments just made
are experiments in the interference of sound.
INTERFERENCE OF SONOROUS VIBRATIONS. 105
EXPERIMENTS IN WHICH, BY THE AID OF A PAPER CONE
AND A RUBBER TUBE, WE FIND OUT THE MANNER IN
WHICH A DISK VIBRATES.
In describing Experiments 27, 28, 29, and 30, we stated
that a vibrating disk always divided itself into an even
number of sectors. This fact was explained by the state-
ae that the adjoining vibrating sectors of the disk were
always moving in opposite directions. The truth of this
ae will be manifest on making the following ex-
periments, which can only be explained by the fact that
adjoining sectors, at the same instant, are always in oppo-
site phases of vibration. These experiments will also
afford beautiful illustrations of the interference of sono-
rous vibrations. ;
Take a piece of cardboard and roll it into a cone about
10 inches long. The small end of the cone should have in
it an opening of such a size that the cone will fit into the
rubber tube used in Experiment 32. If a brass disk of 6
inches in diameter is used in the experiments, the mouth
of the cone should be 24 inches in diameter.
EXPERIMENT 68.—Make the plate vibrate with four
sectors as in A, Fig. 23. Close one ear with soft wax ; into
the other put the end of the rubber tube ; then place the
centre of the mouth of the cone exactly over the centre of
the plate with the cone quite close to its surface. In this
position (which we will call No. 1, for future reference) no
sound is perceived, or at least only a very faint one. This
is so, because in this position of the cone it always receives,
at the same instant, from the vibrating disk, four equal
sound-pulses ; and as two of these are condensations, and
two are rarefactions, they mutually neutralize each other,
106 SOUND.
and the drum-skin of the ear remains at rest and no sound
is perceived.
ExpERIMENT 69.—Now move the mouth of the cone
along the middle of a vibrating sector toward the edge
of the disk. As the cone progresses the sound grows
louder till it reaches its maximum when the edge of the
cone reaches the edge of the disk. In this position (No.
2) the cone receives from the disk only regular sonorous
vibrations, one condensation or one rarefaction alone enter-
ing the disk at a time.
EXPERIMENT 70.—Slowly move the cone along the
circumference of the vibrating disk, keeping the edge of
its mouth close to the border of the disk. The sound at
once begins to diminish in intensity, until the circle of the
mouth of the cone in its progress is divided into two
semicircles by a nodal line. No sound is now perceived,
because in this position (No. 3) a condensation and a rare-
faction enter the ear together, for on the opposite sides of
a nodal line the plate has always opposite directions of
motion. :
EXPERIMENTS WITH BEATING SOUNDS.
~ Exprertment 71.—In purchasing the two A-forks, you
took special pains to get two which were tuned accurately
to unison; otherwise they are of: no value for our experi-
ments. ‘lake one of these in each hand and make them
sound together. Hold them near each other close to the
ear, and you will observe that while both sound there ap-
pears to be but one note. The two sounds blend together
perfectly, so that we cannot distinguish one from the
other. Having tried this thoroughly, place a bit of wax
on the end of one of the forks, and then make them sound
INTERFERENCE OF SONOROUS VIBRATIONS. 107
while each is held upright on its resonant box (see Experi-
ment 41). At once you hear something unusual: little
bursts of sounds, followed by sudden weakenings and loss
of power, as if the forks sang forte and then piano alter-
nately. These singular quivering changes in the tone of
the two forks, when sounded together, are called “ beats.”
The sound seems to beat with a pulse-like motion at regu-
lar intervals. Take off the wax and the beats disappear,
and the two forks sound together like one instrument.
EXPERIMENT 72.—Put on a larger or smaller piece of
wax and the beats change their character, coming faster
or slower each time the amount of wax is changed.
These experiments succeed admirably by using the
tumblers of Experiment 43, or the resonant bottles of Ex-
periments 63, 64, in place of the resonant boxes. The
tumblers or bottles should be carefully tuned, one to the
loaded, the other to the unloaded fork.
To understand these singular beats, you must remem-
ber that each fork sends out sonorous waves, or alternate
condensations and rarefactions, through the air. When
the forks are sounded together (without the wax), each
sends out the same number of waves in a second, and
these travel out together, the condensations and rarefac-
tions of each moving side by side, and reaching the ear
at the same time.
When we loaded one fork with wax we caused it to
move slower. The processions of waves streaming out
from each may start together, but they do not keep to-
gether ; as the loaded fork is going slower its waves of
sound are longer and drag behind. The condensations
and rarefactions no longer travel side by side. A con-
densation from one fork arrives at the ear at the same
time that a rarefaction arrives from the other. Thus
108 SOUND.
they interfere and destroy each other, and the interfer-
ence makes silence, just as we discovered in our last ex-
periments. The condensations and rarefactions from the
two forks continue to arrive at the ear, and soon two con-
densations or two rarefactions come side by side and ar-
rive at the ear together, and they mutually aid or reén-
force each other, and there is a sudden burst of sound as
if the forks were sounding louder.
The waves of sound continue to move, and one set of
waves slips past the other, till the condensations of one set
arrive at the ear alongside of the rarefactions of the other,
and again there is interference and silence. By such con-
tinuous actions beats of sound are produced.
Fie. 41.
Fig. 41 represents two such series of waves traveling
side by side. One series is represented by a full line, the
other by a dotted one. At A the condensations of one
series are shown as opposite the rarefactions of the other ;
but, as the waves represented by the full line are longer
than those represented by the dotted line, the former pass
the latter, so that at C the two series act together, and
we have a beat ; while at a more distant point, B, the
motions in the waves are opposed, and here there is inter-
ference and silence. It is evident that the sliding of the
longer waves past the shorter will cause the waves, meet-
INTERFERENCE OF SON OROUS VIBRATIONS. 109
ing at B, alternately to act together and to interfere ; and
thus the ear, placed at , will perceive beats of sound.
It necessarily follows that, if one fork vibrates 100
times in a second and the other 101 times, there will be
one beat in every second. The number of beats made in
a second is equal to the difference in the number of vibra-
tions per second made by the two vibrating bodies.
oO
a A
110 SOUND.
CHAPTER IX.
ON THE REFLECTION OF SOUND.
PROFESSOR ROOD’S EXPERIMENT, SHOWING THE REFLEC-
TION OF SOUND.
EXPERIMENT 73.—Fig. 42 represents a disk of card-
board 12 or 14 inches in diameter, and having two sectors
cut out of it, on opposite sides of its centre. This is
mounted on the rotator, so that it can be turned round
quickly. Let some one sit beside the rotator so that
he can turn the handle, and at the same time blow a toy
trumpet, which I have found to be the best pipe for this
experiment. Hold the trumpet so that it will be inclined
to the surface of the disk, and with its open end just in
front of one of the openings, as shown in Fig. 42. While
the rotating disk is being turned steadily round, and the
pipe is sounding, go to a distant part of the room, and |
here you will perceive the sound of the pipe changing
rapidly, alternately growing louder and then softer like
beats.
This effect is the result of reflection. When the solid
part of the disk passes before the pipe the vibrations of
sound are reflected or echoed from the card. When the
openings pass before the pipe, part of the vibrations pass
through the open place and are lost, and the sound to the
listener appears to lose power.
REFLECTION OF SOUND. 111
In performing this experiment care must be taken to
place the disk in such a position that the sound will be
reflected to the distant listener. As we learned in our ex-
ZZ
Z
ZZ
Z,
periments in “ Light,” there is a law governing reflections.
We found by our experiments that the angle of reflection
is always equal to the angle of incidence, and the same
law holds good in the reflection of sound.
ExprerimEent 74.—Another experiment in the reflec-
tion of sound may be made with a common palm-leaf fan.
Let some one sound the trumpet at one end of a room,
while you hold the fan upright beside one ear. While
<
112 SOUND.
the trumpet is sounding, twirl the fan slowly by the han-
dle, and you will observe a change in the sound. In cer-
tain positions of the fan the trumpet will sound louder,
and in other positions it will be softened. If you do not
obtain this effect at once, try the fan in several positions
as it stands upright, and, after a few trials, you will ob-
tain a reflection of the sound from the surface of the fan.
The sound of a locust on a warm day, or the beating of
the surf on the shore, or the sound of a distant voice, may
thus be caught on the fan and reflected into the ear.
Echoes are also reflections. The vibrations travel
through the air and meet a building, then the side of a
mountain or hill, and rebound or reécho, perhaps many
times.
EXPERIMENT 75.—You can readily find an echo any-
where in the country by walking near a barn or house and
shouting or singing. The first trial may not bring out
the echo, but, by changing your position, going nearer or
walking farther away, and always standing squarely in
front of the barn or other building, you will soon find the
spot where an echo is heard. We already know that in
winter, when the thermometer is at 82° Fahr., sound
moves at the rate of 1,090 feet in a second. If you stand
at 545 feet from the reflecting wall, and make a short,
sharp sound, it will take one half second for it to go to the
wall, and one half second to come back, and there will be
one second between the sound and its echo.
In our experiments with the tuning-fork and two bot-
tles (see Fig. 40), you remember, we put a piece of card-
board and a flat gas-flame before the mouth of one of the
bottles. Here, also, we had a reflection of the sound from
the cardboard, and even from the flame.
ad
PITCH OF SOUNDS. 1138
CHAPTER X.
' ON THE PITCH OF SOUNDS.
ExprerimmMEnt %6.—Take one of the A-forks and the C-
fork and stick them in the block of wood side by side,
with the opposite prongs of the two forks inclined to
each other, so that by drawing a rod between them they
* will be set vibrating at the same time. Stick a piece of
copper-foil on the tips of the prongs nearest each other,
and arrange the smoked glass and its guide as directed in
Experiment 25. Vibrate the forks by drawing the rod
between them, and obtain the traces of their vibrations on
the smoked glass.
Take the smoked glass and carefully measure off an
equal space on each trace, and then count the vibrations
inclosed in this space. If the right forks have been se-
lected it will be found that 174 vibrations of one fork
cover as much space.as 21 vibrations of the other. From
this you readily see that, in the same time, one fork vi-
brates oftener than the other. Carefully notice which
fork makes the greater number of vibrations. Bring one
vibrating fork to the ear, and then the other, and you will
observe that the C-fork gives a higher note than the A.
The C-fork makes the greater number of vibrations (21)
in a given length on the trace, and the A-fork makes the
smaller number (174) in the same length. We are con-
114 SOUND.
vinced by this experiment that a fork giving a high note
vibrates oftener in a second than a fork giving a lower
note. Experiments on all kinds of vibrating bodies—
solids, liquids, and gases—have proved that the pitch of a
sounding body rises with the increase in the number of
its vibrations in a second. This fact may be stated thus:
The pitch rises with the frequency of the vibrations.
From the above fact it follows that the pitch of a sound
rises with an increase in the number of sonorous waves
that reach the ear in a second.
EXPERIMENTS WITH THE SIREN.
Fig. 43 shows an instrument called a siren. I will
show you how to make several instructive and curious
experiments with it. First, you will find out the number
of vibrations made in a second by a sounding body like
one of your tuning-forks ; and, having found out this,
you will use the fork to determine for yourself the veloc-
ity of sound. The siren will also tell you this important
fact: That the numbers of vibrations per second which
give the various notes of the gamut, or musical scale, bear
_ to each other fixed numerical relations.
To make the siren, get a piece of cardboard, or mill-
board, and draw on it with a pair of dividers a circle
83 inches (21.6 centimetres) in diameter; then cut this
circle out of the cardboard. Now draw four circles, the
inner one with the legs of the dividers opened to 2} inches
(5.73 centimetres), the next with a radius of 22 inches
(6.99 centimetres), the third with 34 inches (8.26 centi-
metres), and the fourth with 33 inches (9.53 centimetres).
Divide the circumference of the outer circle into 24 equal
parts, and to each of these points of division draw a line
from the centre, as shown in Fig. 44. Divide the spaces
PITCH OF SOUNDS. 115
on the outer circle in halves; this will give 48 points on |
this circle. At each of these points cut a hole of about
a iV
Well
v1
an LATTaae 3
—_ =
a
7s Inch (5 millimetres) in diameter with a punch. Then
punch holes at the 24 points on the inner circle.
The student, on looking at Fig. 44, will see that, on
the radii marked 1, 2, 3, 4, 5, and 6, the holes are all in a
116 SOUND.
line. These holes, thus in line, divide the circle into six
equal parts. Divide each of these sixths on the second cir-
cle into five equal parts, and each sixth on the third circle
into six equal parts, and through each of these points of
division cut a hole with the punch. By following these
directions you will have made on the inner circle 24
holes, on the second 380, on the third 36, and on the fourth
48 holes.
Now cut a hole in the centre of’ the disk, so that it
neatly fits on the screw of the small pulley of the rotator
PITCH OF SOUNDS. 117
shown in Fig. 43. Then put into a piece of India-rubber
tube a glass tube having its interior about the diameter
of the holes in the card disk. We are now ready for our
experiments.
EXPERIMENT 77.—Rotate the disk slowly, and, placing
the glass tube before a ring of holes, blow through the
tube. You will observe that whenever a hole comes be-
fore the tube a puff of air goes through the disk. If the
disk is revolved faster the puffs become more frequent,
and soon, on increasing the velocity of the disk, they blend
into a sound. Not very pure, it is true; but yet, in the
midst of the whizzing, your ear will detect a smooth note.
Fixing your attention on this note, while the rotator is
urged with gradually increasing velocity, you will hear
the note gradually rising in pitch. This again shows us
that the pitch of a sound rises with the frequency of the
vibrations causing it.
Two bodies make the same number of vibrations in a
second when they give forth sounds of the same pitch.
Therefore, if we can measure how many vibrations the
disk makes in a second while it gives the exact sound of
one of the forks, we will have measured the number of
vibrations which the fork makes in asecond. If we count
with our watch ‘the number of turns the crank C makes in
one minute, we can from this knowledge calculate the
number of puffs or vibrations the disk makes in one sec-
ond, as follows: One revolution of the crank of the rota-
tor makes the disk go round exactly five times. Now,
suppose that the tube is before the third circle, having 86
holes, and that in. one minute the crank C turns round
100 times. Then in one minute the disk turned 5 times
100 times, which is 500 times. But for each turn of the
disk 36 puffs or vibrations were made on the air ; there-
118 SOUND.
fore, 36 times 500, or 18,000, puffs or vibrations were
made by the disk in one minute, and 7, of 18,000, or 300,
in one second.
But it is difficult to know just when the disk gives the
same sound as the fork, and it is yet more difficult to keep
the disk moving so that it holds this sound, even for a few
seconds. ‘To do this, very expensive apparatus has here-
tofore always been needed. But I did not wish to ban-
ish from our book such an important experiment, so I
found out a cheap and simple way of doing it, which I
will show you.
EXPERIMENT WITH THE SIREN, IN WHICH -IS FOUND THE
NUMBER OF VIBRATIONS MADE BY A TUNING-FORK IN
ONE SECOND.
ExPERIMENT 78.—Get a glass tube (the same we used
in the experiment on page 50 of “ Light ”) # inch (19 milli-
metres) in diameter and 12 inches (30.5 centimetres) long,
-and a cork 1 inch thick, which slides neatly in the tube.
Put the cork into one end of the tube, and holding a stick
upright press the cork down on it. The fork is now vi-
brated and held over the open end of the tube, while the
cork is forced up the tube with the stick till the column
of air in the tube is brought into tune with the fork.
This you will know by the tube sending out a loud sound.
Try this several times till you are sure of the exact place
~where the cork should be to make the tube give the loud-
est sound.
Now lay the fork aside, and with small pieces of wax
stick the tube on the top of a block, or on a pile of books,
with its mouth near the disk and facing one of the cir-
cles of holes, as shown in Fig. 43. On the other side
PITCH OF SOUNDS. 119
of the disk, and just opposite the mouth of the resonant
tube, hold the small tube through which you blow the air.
Turn the crank at first slowly, then gradually faster
and faster. Soon a sound comes from the tube. This
gets louder and louder ; then, after the disk has gained a
certain speed, the sound grows fainter and fainter, till no
sound at all comes from the tube.
When the sound from the tube was the loudest, the
disk was sending into the tube the same number of vi-
brations in a second as the fork makes ; for the tube was
tuned to the fork, and can only resound loudly when it
receives from the disk of the siren the same number of
vibrations in a second as the fork gives.
It is, then, quite clear that, to find out the number of
vibrations per second given by the fork, we first have to
bring the disk to the velocity that makes the tube sound
the loudest, and then to use this sound as a guide to the
hand in turning the crank of the rotator. Practice will
soon teach the hand to obey the check given by the ear ;
_ and if the student have patience, he will be rewarded when
he finds that he can keep the tube: sounding out loudly
and evenly for 20 or 30 seconds. Then we count the
number of turns made by the crank-handle OC of the rota-
tor in 20 or 30 seconds of the watch. If we have suc-
ceeded in this, we can at once calculate the number of
vibrations the fork makes in one second.
The following will show how this calculation is made :
Experiment 79.—The cork was pushed to that place
which made the air in the tube resound the loudest to the
A-fork. The tube was then placed facing the circle of 36
holes. After we had succeeded in making the tube re-
sound loudly.and evenly to the turning disk, I counted the
number of turns I gave to the handle C in 20 seconds,
6
120 SOUND.
and I found this number to be 49. For one revolution of
the handle C, the disk makes exactly five. Hence 5 times
49, or 245, is the number of turns the disk made in 20 sec-
onds. But in one turn of the disk 36 puffs or vibrations
entered the tube; therefore, 245 times 36, or 8,820, is the
number of vibrations that went into the tube in 20 sec-
onds; and 3, of 8,820, or 441, is the number of vibra-
tions which entered the tube in one second.
The experiment, therefore, shows that the tube resounds
the loudest when 441 vibrations enter it in one second.
But the tube also resounded its loudest when the vibrating
A-fork was placed over it. Hence the A-fork makes 441
vibrations in one second. ;
ExpPERIMENT 80.—Let the student now try to find out
by a like experiment the number of vibrations made by
the C-fork in one second. Repeat these trials many times
till numbers are found which do not differ much from one
another.
' FINDING THE VELOCITY OF SOUND BY AN EXPERIMENT
WITH THE TUNING-FORK AND THE RESONANT TUBE.
ExpERIMeNT 81.—Our experiment (78) with the glass
tube has taught us that the tube must have a certain depth
of air in it to resound loudly to the A-fork. Let us meas-
ure this depth. We find it to be 7% inches (19.47 centi-
metres) when the air has a temperature of 68° Fahr.
From this measure, and from the knowledge that the
A-fork makes 441 vibrations in one second, we can com-
pute the velocity of sound in air.
It is evident that the prong of the fork over the mouth
of the tube, and the air at the mouth of the tube, must
swing to and fro together, otherwise there will be a strug-
PITCH OF SOUNDS. 121
gle and interference between these vibrations, and then
the air in the tube cannot possibly co-vibrate and strengthen
the sound given by the fork. —
We have already learned that the prong of the fork
in going from a to b, Fig. 45, makes one half wave-length
in the air before it. This may be represented by the
curve 6 cd above the line 6 d. Now the tube 7’ must be
as long as from 6 to ¢, or one-quarter of a wave-length ;
so that, by the time the prong of the fork has gone from
a to b, and is just beginning its back-swing from 6 to a,
Fig, 45.
the half-wave 6 c d has just had time to go to the bottom
of the tube 7; to be reflected back, and to reach the prong
b at the very moment it begins its back-swing. If it does
this, then the end of this reflected wave (shown by the
dotted curve in the tube 7’) moves backward with the
back-swing of the prong 0, and thus the air at the mouth
of the tube and the prong of the fork swing together, and.
the sound given by the fork is greatly strengthened.
If the depth of the quarter of the wave made by the
A-fork is 7% inches (19.47 centimetres), the whole wave is
122 SOUND.
30.64 inches, or 2.55 feet (77.88 centimetres). But we
have already learned that, when the A-fork has vibrated
for one second, it has spread 441 sonorous waves all
around it. As one wave extends 2.55 feet (77.88 centi-
metres) from the fork, 441 waves will extend 441 times
2.55 feet (77.88 centimetres), or 1,124 feet (342.6 metres).
This is the distance the vibrations from the A-fork have
gone in one second. In other words, this is the velocity
of sound in air at 68° Fahr., as found out by the fork and
resonant tube.
Thus we find that the most modest apparatus, when
used with patience and thoughtfulness, can solve problems
which, at first sight, may appear far beyond our power.
The cardboard siren, the little tuning-fork, and the glass
tube have measured the number of vibrations of the fork
and the velocity of sound.
EXPERIMENT 82.—In a similar manner let the student
determine the number of vibrations of the C-fork, and
then with it and the resonant tube let him measure the
velocity of sound, and compare this result with that found
with the A-fork.
' THE NUMBER OF VIBRATIONS PER SECOND, GIVEN BY RES-
ONANT TUBES AND ORGAN-PIPES, IS INVERSELY AS
THEIR LENGTHS.
If the number of vibrations per second of the fork be
doubled, the sonorous waves which it makes will be short-
ened one-half; hence the resonant tube must be shortened
one-half in order to resound to the fork. If the num-
ber of vibrations of the fork are half as frequent, it will
make sonorous waves twice as long ; hence the tube to re-
sound to this fork must be doubled in length. These facts
PITCH OF SOUNDS. 123
are stated in the following law: The lengths of resonant
tubes are inversely as the numbers of the vibrations to
which they resound.
But organ-pipes are merely resonant tubes whose col-
umns of air, instead of being vibrated by a tuning-fork,
are vibrated by wind passing through a mouth-piece ;
hence the following law: The lengths of organ-pipes are
inversely as the numbers of vibrations which they give in
a second, .
124 | SOUND.
CHAPTER XI.
ON THE FORMATION OF THE GAMUT.
EXPERIMENTS WITH THE SIREN, SHOWING HOW THE SOUNDS
OF THE GAMUT ARE OBTAINED.
Tue disk of our siren has four circles of holes. The
innermost or first circle contains 24 holes, the second. 30,
the third 36, and the fourth or outermost circle has 48
holes.
EXPERIMENT 83.—Turn the handle of the rotator even-
ly and steadily, and at a moderate speed, and, while
blowing through the tube, move it quickly from the
inner ring of holes to the next, then to the next, and
finally to the outer ring of holes. No experiment yet
made brings so pleasant a surprise as this one. We
have already found that the pitch of sound rises with
the increase in the frequency of the vibrations caus-
ing it. As the tube moves from the first to the fourth
circle, more holes successively pass before it in one turn
of the disk ; therefore the pitch rises suddenly as the tube
reaches each circle in order. But, more than this, the
successive sounds evidently have a familiar musical rela-
tion to each other, and this musical relation is not changed
by turning the disk more or less rapidly. The pitch of
the notes is thereby changed, but the same musical rela-
FORMATION OF THE GAMUT. 125
tion exists no matter how swiftly the disk turns during
the experiment.
EXPERIMENT 84,—A few trials will convince you that,
when you sing the notes DO, MI, SOL, DO, you produce
sounds which follow each other with precisely the same
musical intervals as when you blow air in order through
the 24, 30, 36, and 40 holes in the disk. You have reached
a grand truth lying at the very foundation of music.
Your experiment tells you that, if four sounds are made
by vibrations whose numbers per second are as 24: 30:
36: 48, then these sounds will be those of four notes
which bear to each other the same musical relation as
exists among the notes DO, MI, SOL, DO. In other words,
these four sounds will be the four sounds of what musicians
call the perfect major chord.
Examining the numbers 24, 30, 36, and 48, we see that
each of them may be divided by 6. Doing this, we obtain
the four numbers 4, 5, 6,and 8. The ratios 4:5:6:8 are
the same as held among the other numbers, but are simpler
and easier to remember. Thus the perfect major chord
will always be produced, if the ratios of the vibrations per
second of four sounds are as 4:5:6: 8.
EXPERIMENT 85.—By blowing first into the circle of
24 holes and then into the circle of 48 we hear two notes.
The second is the octave of the first, and the fact is uni-
versally true that the octave of any sound is obtained by
doubling the number of its vibrations.
With our siren we have just found out the relations of
the numbers of vibrations per second which make the four
sounds of the perfect major chord. But this simple instru-
ment has even greater capacity than this. It can give us
those related numbers of vibrations which form all the
sounds of the gamut.
126 SOUND.
From the proportion 4 : 5 : 6 are derived all the sounds
of the musical scale. These numbers form the very
foundations of harmony. ‘They should be engraved on
the pediment of the temple of music.
It has been discovered by experiment that the numbers
of vibrations giving the notes of the gamut, or, more
properly, the sounds of the natural scale of music, are re-
lated as is shown in the following proportions :
(1)? te OO: Ce tk ssa.
(2) “pe 2) -ohOuue fare cts sale
(3) 46 De-4 cic A ae,
Small c and d stand for the notes of the octave above
C and D.
To form the gamut from these proportions, we must -
decide on the number of vibrations per second which
shall give the sound C or DO. Let 264 vibrations per
second be fixed as giving the C or DO of the octave below
Then Proportion (1) becomes
C:E:G::4:5:6: : 264: 330: 396,
Proportion (2) becomes
G:B:d:34:5: 6% : 396: 495 : 594.
Proportion (3) becomes
Ct AL Bi) 6:25 4) 528 24400 352,
Thus, by starting the first number of Proportion (1)
with C, equal to 264 vibrations, we find that G will be
given by 396 vibrations. Then starting Proportion (2)
with G, equal to 396 vibrations, we find that B and the
octave above D will be given by 495 and 594 vibrations.
FORMATION OF THE GAMUT. 127
Therefore D is equal to one-half of 594, or 297. We start
Proportion (8) with c, of 528 vibrations, the octave above
C, and we obtain the numbers of vibrations per second
which give the sounds A and F,
We here write in their proper order these notes of the
gamut, and place under them their numbers of vibra-
tions. The notes of the gamut are also designated as Ist,
2d, 3d, 4th, etc., so as to indicate what are called znter-
vals, ‘Thus the G forms to the C the interval of the 5th.
The E is the interval of the 3d to C.
—— SS
ee Ae
264 297 330 352 396 440 495 528
1st 2d 3d 4th Sth 6th ‘7th 8th.
An examination of these numbers will show that each
may be divided by eleven. Doing this, we obtain the fol-
lowing series of numbers, which gives the relative numbers
of the vibrations for the notes of the gamut in any octave
of the musical scale :
Cre lor Wie Gee Asch Dia C
24: 27: 30: 832: 36: 40: 45: 48.
ExprRIMENT 86.—Of the correctness of the above
mode of forming the gamut, you may convince yourself
by cutting another disk for the siren having eight in-
stead of four circles of holes, each circle having, in order,
these numbers of holes, viz.: 24, 27, 30, 32, 36, 40, 45, 48.
Turning the disk, by giving to the crank a uniform mo-
tion of 22 revolutions in 10 seconds, while you succes-
sively blow into the circles, you will hear in succession
the eight notes of the gamut of the octave of C, of 264
vibrations,
128 SOUND.
EXPERIMENT 87.—Even the disk with four circles of
holes may be made to give all the notes of the gamut, but
only four notes in each experiment.
You will find on making the calculation that, if you
turn the handle of the rotator 22 times in 10 seconds, you
will make the C of Proportion (1); 33 turns in 10 seconds
will give the G of Proportion (2); while 294 turns in 10
seconds will give the F of Proportion (3). Hence, if you
blow into the four circles of holes, while the disk has in
succession these three different velocities, you will succes-
sively get the numbers of vibrations making the sounds
of the gamut given in Proportions (1), (2), and (8).
EXPERIMENTS WITH THE SONOMETER. 129
“ CHAPTER XII.
| EXPERIMENTS WITH THE SONOMETER, GIVING THE
SOUNDS OF THE GAMUT AND THE HARMONICS.
Fic. 46 represents a wooden box 59 inches (150 centi-
metres) long, 43 inches (12 centimetres) wide, and 43
inches (12 centimetres) deep. The sides are made of oak
Fie. 46.—The Sonometer.
$4 inch (12 millimetres) thick, and the two ends of oak
1 inch (25 millimetres) thick. These are carefully dove-
tailed together. In the side-pieces are cut three holes, as
shown in the figure. There is no bottom to the box, and
the top is made of a single piece of clear pine 4 inch (3
millimetres) thick, and glued on. Two triangular pieces,
4 inch (2 centimetres) high, and glued down to the cover
of the box, just 474 inches (120 centimetres) apart, form
bridges over which the wires are stretched. There is
also, as shown at Z, a loose piece of pine 24 inches (6.35
130 SOUND.
centimetres) wide, 4 inch (2 centimetres) thick, and about
43 inches (12 centimetres) long. At a, 6 are two screw-
eyes set firmly upright at one end of the box in the oak.
At c,d are two piano-string pegs. From these to the
screw-eyes are stretched two pieces of piano-forte wire
(No. 14, Poehlemann’s patent, Nuremberg). In putting
on these wires, the ends must be annealed, by making
them red-hot in a stove, before they are wound round the
screw-eyes or pegs. Such an instrument is called a so-
nometer, and will make a useful and entertaining instru-
ment for our experiments. When it is finished, the wires
may be drawn up tight by means of a wrench or piano-
tuner’s key, and then we shall find, on pulling the wire
one side and letting it go, that it gives a clear tone that
lasts some time.
EXPERIMENTS WITH THE SONOMETER, GIVING THE SOUNDS
OF THE GAMUT.
ExPERIMENT 88.—Place the sonometer (Fig. 46) in front
of you, and with a metric measure lay off distances from
the left-hand bridge to the right, of 60 and 30 centimetres,
Tighten the wire till it gives, when plucked, a clear musical
sound, not too high in pitch. Then place the block #
(Fig. 46) under the wire, with its edge on the line marked
60 centimetres, and place the end of the finger on the wire
at this edge of the block. Pluck the wire at the middle
of this length of 60 centimetres, and listen attentively to
the pitch of the sound. Then at once remove the block
and pluck the wire in its middle so that the whole wire
vibrates. You will perceive that the sound now given
is like the one given when the half-wire vibrated, only it
EXPERIMENTS WITH THE SONOMETER. Ist
differs in this, it is the octave below it. With the block
placed at 30 centimetres, vibrate one-quarter of the length
of the wire, and you will find that we have the sound
of the first octave above that made by half the wire,
and the second octave above the sound given by the
whole wire.
Our siren has proved that by doubling the number of
vibrations the sound rises an octave. Therefore, when a
wire is shortened one-half -it vibrates twice as often, and
when shortened one-quarter it vibrates four times as often,
as when its whole length vibrates. This then is the rule, or
law, which governs the vibrating wire. The force stretch-
ing the wire remaining the same, the numbers of vibrations
of the wire become more frequent directly as its length is
shortened. Thus, if the wire be shortened 4, 4, 4, or 4,
the number of its vibrations per second will increase 2, 4,
3, or 9 times.
EXPERIMENT 89.—Knowing this law we can readily
stretch a wire on the sonometer till it gives say the C of
264 vibrations per second, and then determine the various
lengths of this wire which when vibrated will give all the
notes of the gamut. We have seen that the relative num-
bers of vibrations which give the sounds of the gamut
are as follows:
LiPi a OE etl ee aenliage grin” SR Ries Me Case Be ke GaAs Boe
Relative number of vibrations... 24 27 380 32 36 40 45 48
Lengths of wire (in centimetres).120 1063 96 90 80 72 64 60
We have seen that, if the whole length of 120 centi-
metres of wire gives C, then 60 centimetres must give c of
_ the octave above, and, as the relative numbers of vibrations
of G and C are to each other as 86 is to 24, it follows that
the length of the C-wire must be longer than the G-wire
1382 SOUND.
in the ratio of 36 to 24. Hence the proportion 36 : 24
: : 120: 80 gives 80 centimetres as the length of the G-
wire. In like manner the lengths of wire which give the
other sounds of the gamut have been calculated. In the
third line of the above table we have given these lengths
in centimetres. Lay off these lengths on the sonometer,
always measuring from the left-hand bridge toward the
right, and draw lines across the top of the sonometer
through these points of division and letter them in order
D, E, F, G, A, B,c. If you now place the block # (Fig.
46) successively at these divisions, and vibrate the frac-
tions of the wire so made, you will obtain in succession
the notes of. the gamut. |
EXPERIMENTS WITH THE SONOMETER, GIVING THE HAR-
MONIC SOUNDS.
There is another series of sounds called the harmonic
sounds,in which the relative numbers of the vibrations
making them are as 1:2:3:4:5:6:7:8:9: 10, ete.
The law ruling the vibrations of wires and strings teaches -
us that this series of sounds will be given by the sonome-
ter if we vibrate its wire after it has been successively
shortened 4, 1, 4, 4, 4, 4, 4, 4, x, etce., of its: whole
length.
EXPERIMENT 90.—Again place the sonometer before
you, and taking the metric measure divide the length of
the top between the bridges into 4, 4, 4, 4, 4, 4, 4, 4, + of
120 centimetres. This is done by measuring in order,
from the left-hand bridge (Fig. 46) toward the right, 60,
40, 30, 24, 20, 17.14, 15, 13.33, and 12 centimetres. Draw
lines through these points of division across the top of the
EXPERIMENTS WITH THE SONOMETER. 133
sonometer, and number them in order 4, 4, 4, 4, 4, 4,
. zo:
Now place the block /' at each of these lines of divis-
ion and vibrate the successive fractions of the wire, and
you will have produced in order the sounds of the har-
“monic series.
If we make the whole string vibrate the sound
Colm
3
of 66 vibrations per second, then the harmonic series
of this C will be as follows. The numbers of vibra-
tions are written under the names of the notes. The
latter are given in letters accented to indicate the
octaves.
a a eS
SS SSS
Ot ees oe er te bh Ten gin Fy
66 1382 198 264 330 396 462 528 594 660
ee te ape te A Sy ee frye oe eB oer Ob. = 10)
_ The lowest sound of a harmonic series is called
by the names of fundamental, or first harmonic, or
prime. The other sounds are known as the 2d, 3d,
4th, etc., harmonic, or as 1st upper partial tone, 2d
upper partial tone, etc., or as Ist, 2d, 3d, etc., har-
monic overtones.
The harmonics of the wire may be obtained in other
134 ' SOUND.
ways, making the following series of beautiful experi-
ments :
A Vv ne uv’ B
<<<
a
a n Vv n’ ue
Ae eee
}
aw n vw nr v nr oe"
4.
Vv Tu w n ar n uw n’
Fig. 61.
vuleanite, B B, with a hole in its centre. The under
side of this disk nearly touches the plate A. Its upper
surface is cut into a shallow, funnel-shaped cavity lead-
ing to the opening in its centre.
172 TALKING MACHINES.
To operate this machine we first neatly coat the cylin-
der with a sheet of foil; then we bring the point P to
bear against this foil, so that, on turning the cylinder, it
makes a depressed line or furrow where the foil covers
the space between the threads cut on the surface of the
cylinder. The mouth is now placed close to the open-
ing in the vulcanite disk B Bb, and the metal plate is
talked to, while the cylinder is revolved with a uniform
motion.
The thin iron plate A vibrates to the voice, and the
point P indents the foil, impressing in it the varying num-
bers, amplitudes, and durations of these vibrations. If the
vibrations given to the plate A are those of simple sounds,
then they are of a uniform regular character, and the
point P indents regular undulating depressions in the foil.
If the vibrations are those causing complex and irregular
sounds (like those of the voice in speaking), then simi-
larly the depressions made in the foil are complex (like
the curve of Fig. 49) and irregular. Thus the yielding
and inelastic foil receives and retains the mechanical im-
pressions of these vibrations with all of their minute and
subtile characteristics. } |
Our experiment No, 121 has, however, taught us that
the forms of these impressions will change with every
change of distance of the place of origin of the com-
pound sound from the vibrating plate A, even when at
these various distances the compound sonorous vibrations
fall on the plate with precisely the same intensity. Hence
the futility of attempting to read sound-writings.
The permanent impressions of the vibrations of the
voice are now made. It remains to show how the opera-
tion just described may be reversed, and thus to obtain -
Jrom these impressions the aérial vibrations which made
SOUND. : 173
them. Nothing is simpler. The plate A, with its point P,
is moved away from the cylinder by pulling toward you
the lever H G. Then the motion of the cylinder is re-
versed till you have brought opposite to the point P the
beginning of the series of impressions which it has made
on the foil. Now bring the point up to the cylinder ;
place against the vulcanite plate B £6 a large cone of
paper or of tin to reénforce the sounds, and then steadily
turn the crank J). 'The elevations and depressions which
have been made by the point P now’ pass under this
point, and in doing so they cause it and the thin iron
plate to make over again the precise vibrations which
animated them when they made these impressions under
the action of the voice. The consequence of this is,
that the iron plate gives out the vibrations which pre-
viously fell upon it, and 7 talks back to you what you
said to it.
174 TWARMONY AND DISCORD.
CHAPTER XIX.
ON HARMONY AND DISCORD. A-SHORT EXPLANA-
TION OF WHY SOME NOTES, WHEN SOUNDED TO-
GETHER, CAUSH AGREEABLE AND OTHERS DISA-
GREHEABLE SENSATIONS.
Ir, toward sunset, you walk on the shady side of a
picket-fence, flashes of light will enter your eye every time
you come to an opening between the pales. These flashes,
coming slowly one after the other, cause a very disagree-
able sensation in the eye. Similarly, if flashes or pulses
of sound enter the ear, they cause a disagreeable sensa-
tion. Such pulses enter the ear when we listen to two
sounding organ-pipes, two forks, or two wires on the so-
nometer which are slightly out of tune with each other.
As you already know (see Experiment 71), these flashes
or pulses of sound are called beats. You also know that
the number of these beats made in a second is equal to
the difference in the numbers of vibrations made in one
second by the two sounding bodies. Thus, if one sound-
ing body makes 500 and the other 507 vibrations in a
second, then 7 beats per second will be heard.
EXPERIMENT 127.—With your toy trumpet and the
disk used in Rood’s experiment in the reflection of sound,
Fig. 42, you can make an excellent experiment, showing
the effects of beats on your ear. Sound the trumpet, and
SOUND. 1%5
gradually increase the velocity of the turning disk. At
first the beats of sound so caused may be separately dis-
tinguished by the ear, and, though not pleasant in their
effect, yet they can be endured. As the frequency of the
beats increases, the harshness of the sensation becomes
greater and greater, until the effect on the ear becomes
actually painful.
But, if the flashes of ight or beats of sound aceeed
one another so rapidly that the sensation of one flash or
beat remains till the next arrives, you will have continu-
ous sensations that are not unpleasant. In other words,
continuous sensations are pleasant, but discontinuous or
broken sensations are disagreeable.
If two sonorous vibrations reach the ear together and
make a disagreeable sensation, then we may be sure that
the Wi irerante in the numbers of their vibrations gives_a
number of beats per second which do not follow one an-
other with sufficient rapidity to blend into a smooth, un-
broken sensation. In other words, these beats are so few
in a second that the sensation of one disappears before the
next arrives, and so discord is the sensation ; but, if the
frequency of the beats be sufficiently increased, the sensa-
tion of one remains till the next arrives, and the sensation
is continuous, and we say that the two sounds are in
harmony. :
Therefore it at once appears that, if we only can find
out the number of beats required in a second to blend
sounds from different parts of. the musical scale, we shall
be able to state beforehand what notes when sounded
together will make harmony and what notes will make
discord.
By many experiments I have found the number of
beats per second that two sounds must make to be in har-
176 HARMONY AND DISCORD.
mony. In the following table a few of the results of
my experiments are given :
Vv B or
N
C 64 16 as = -0625 sec.
c 128 26 zy = .0384 “
e' 256 44 jy = 0212 «
g 384 60 as = 0166 “
c" 512 48 de = .0128 “
e” 640 90 oy —- 201 lee
g" 768 109 sig = 0091 “
e” 1024 135 sis = 0074
Column N gives the names of the notes given by the
vibrations per second in Column V. The c’ in this series is
that used by physicists generally, and gives 256 vibrations.
In Column B is given the smallest number of beats per
second which the corresponding sound must make with
another in order that the two may be in harmony, or,
as it is generally stated, may make with the other the
nearest consonant interval. If 47 beats per second of c’,
for example, blend, then the sensation of each of these
beats remains on the ear 7; of a second. In Column D
are given these durations in fractions of a second. As
these fractions are the lengths of time that the sensation
of sound lingers in the ear after the vibrations of the
air near the drum-skin of the ear have ceased, they are
very properly called the durations of the residual sono-
rous sensations.
You observe in the table that this duration becomes
shorter as the pitch of the sound rises. Thus, while the
residual sensation of C is 7; of a second, that of c’”’ is
only +4;.
Let us use the knowledge thus acquired by making it
aid us in a few calculations and experiments. The table
SOUND. 177
shows that if ce’ is sounded with a note which makes with
it 47 beats in a second, then these beats will fuse into one
smooth, continuous sensation, and the notes must be in
harmony. What is this note? It is found in this man-
ner: c’ is made by 256 vibrations per second, and the
note which will make just 47 beats with it in a second
must make 256+ 47 or 303 vibrations in a second. This
number of vibrations makes a sound a little lower in pitch.
than be’. ‘This is the minor third of c’.
ExpERIMENT 128,—Now let one sing c’ while another
sings be’, and you will find that these sounds form an in-
terval which is just within the range of harmony.
EXPERIMENT 129.—Sing c’ and e’, then c’ and g”, and
you will have yet more pleasant and smooth sensations.
ExrErRmMENT 130.—But if one sings c’ while another
sings d’ you have decided discord, an unpleasant rasping
sensation in the ears. The reason of this is at once ap-
parent : c’ makes 256 while d’ makes 288 vibrations in a
second, and 288 less 256 gives 32 as the number of beats
made in a second; but the table shows that 47 are needed
in a second so that they may follow each other quick
enough to blend.
Making similar calculations throughout five octaves,
we have found the nearest consonant intervals for the c of
each octave from C toc’. These are here given. It will
be observed that this interval contracts as we ascend the
musical scale—a fact which has been well established.
The nearest consonant interval of C is its major third.
i 5 re “¢ “ minor third.
* “ ¢’ “ minor third, less 14 semitone.
‘ 79 6c (79 tt ce 6c 66 “ce
ce ¢ c 7A
iT “ cc cc a“ el” cc second.
wo é - “ civ “ second, less 14 semitone.
178 HARMONY AND DISCORD.
Our experiments in sound have led us into music. We
find that fundamental facts and laws of harmony may be
explained by physiological laws—by rules according to
which our sensations act. Music is the sequence and con-
course of sounds made in obedience to these laws. The
explanation of many of these may be beyond our power ;
for the connection existing between esthetic and moral
feelings and sensations which cause them remains be-
hind a veil. But it may be imagined that distant ages
may bring forth man so highly organized that he may
find his pleasure and pastime in
“ Untwisting all the chains that tie
The hidden soul of barmony.”
- THE END,
List of Apparatus used in the Experiments on Light
and Sound, with the prices, as supplied by Samuel
Hawkridge, successor to George Wale § Co., Ho-
boken, New Jersey.
ibahCalahst
Pipirsaktee ee ee ie cera aha ate A okb Aes ch sca aatE Le eR a $5 00
Water-lantern,........ Peet Nar B a hase ssh eh cia wie gh da ainda ate a 5 00
Bethe Cn cure creer estas aly eee Pees SAS Gis Suey emp eae exes Bf ED
eT tee cet Pe eats ae teeing there coats ors on suets 2G o'h'g © SON 05
Square bottle for refraction........... Sa eae oie ats Fate OMe 15
EA IOUN VCR: FOU, ie ae rar a en le ele ai ation, acne to a haar aly « 75
pmall double-qouvon seman spas wales a gee weng heed vs > liners 50
Flask for condenser of solar microscope. . le 75
Glass cylinder for experiment of the ‘ifemntaved Fete he. ea
with plano-convex lens in place of the large flask shown in
Mt itr cea teat mek A ol ated aie La ate ace’ alare' bv o/ dig WA xhagers 's 1 50
een DV IGUE coi. kade ieee Ri e)s hed gyn eee cae e's #80 aie sores © a 50
Oe, edna sos geet oases oe, fhe ee ee tae vile Wises gee hee 10
Salcerol VeLMuiot DAE ae ea fcr ttea Uike alert incite Cewy Sdis ele Syn > 15
Cake of emerald green paint... .......60.0ecceeees Ce At Pee 15
Nuremberg violet, in powder, to be used with gum-water......... 15
Two small slips of clear glass............... re aaa ads + fade 05
$14 85
SOUND.
1. Heliostat, }
2. Water-lantern, the same as under “ Light.”
2. Plano-convex lens, .
Peatverurn-Dall and: fie WilCow. ons Series ok ce Pere w et oiewe ees $ 05
18. Blackburn’s double pendulum.............. ray erat tee ee 2 50
Pe rerOL WOON aNd Oat e ak aerate 2 6 a aks o dlrab les a slue-eagpe o> 25
ie EeigecOa fine TOMS, [OP VIDTAUGEs ois ds 0 Ales halo lene tale ae eo 25
17. Boxes, to be half filled with sand, for supports.............. 1 00
Eve wor pine roday Witt MiTorase. Phe eu 665 o eaie e's 28 PAN 30
Pm ROH PTs Meet cia Pie ae tte as ates Calais dah Kats Sonne ae 75
180
49. “Tick for fo6tiori fork. 20 ees ae eee bt ks cate ee $ 10
25. Wedden slide and block for fork: .2. 5.2. 3) Studs bo ee ee ee on 25
27. Brass disk for Chladni’s figures. ...........+ wa aA eee 1 00
S24 Tin flute &, 0, ds. Slee Se bis See cats Coa wein ce oisek 15
33. Kundt’s experiment with whistle and tube containing silica... 30
34, Glass tube, 3 feet long, inch in diameter................. 10
40. .Lovers’ telephone... 2.4 smitty aoe % oes ee shellac lgawialo copes 25
64. Two resonant bottles with glass plates...............000. 15
47. Organ pipe-As cis 656 6. belnts 6 o's Whe Clale be ote oresete te eos)
54. Geyer’s sensitive-flame.. .<..).52.5545.5 .c ves bens edune ee 1 00
55. Wooden railway and seven glass marbles.............00-6-. 1 50
57. Long brass spring-cord and resonant box.............---- 1 50
58. Rotator, with four disks, viz., siren, Crova’s, Rood’s, and
Maser a, (8.4545 ole > ainis) fev oiea tiene tae tinnes 10
31. Lycopodium, 2 OUNCES 2. nis sss Vi osles ncele ee ss menbeam an 10
83. Silica powder, in J-onnce bottle. 1.2... . 4-4. oi oe eee
25. Copper-toll i. cates » oste ete wins a eine vine #nit aoe eek s Sees 05
9/ Camel S-hdiriiercl (oe LoS ae tate tas erciye + 3 'e ctete me wee eee erie oe OS
24 SL AD-EOLL. «2% +. ctorate Seo ee cebrle om nists ae tis ne Renee ate coe 10
$27 50
The numbers prefixed to the above list refer to similarly numbered
experiments in “ Sound ” in which these articles are used.
THE EXPERIMENTAL SCIENCE SERIES.
SOUND:
A Series of Simple, Entertaining, and Inexpensive Experiments in the
Phenomena of Sound, for the Use of Students of Every Age.
By ALFRED MARSHALL MAYER,
Professor of Physics in the Stevens Institute of Technology; Member of the
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UNIFORM WITH ‘LIGHT,’ FIRST VOLUME OF THE SERIES.
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D. APPLETON & CO., Pusiisuers, 549 & 551 Broapway, N. Y.
[EPR Ge lesguil 3
A SERIES OF SIMPLE, ENTERTAINING, AND INEXPENSIVE EX-
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USE OF STUDENTS OF EVERY AGE.
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‘It supplies a large number of simple and entertaining experiments on the phe-
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q
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