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SOUND



A. COURSE OF



EIGHT LECTUEES



DELIVERED AT



THE ROYAL INSTITUTION OF GREAT BRITAIN



BY



JOHN TYNDALL, LL.D. F.R.S.

PROFESSOR OP NATURAL PHILOSOPHY IN THE

KOYAL INSTITUTION AND IN THE ROYAL

SCHOOL OF MINES.




NEW YORK:
D. APPLETON AND COMPANY,

443 & 445 BEOADWAY.

1867.



T?



of
. MY FRIEND

RICHARD DAWES

LATE a D X EAN _OF HEREFOK D

i*



1867



PREFACE.



IN the following pages I have tried to render the science
of Acoustics interesting to all intelligent persons, including
those who do not possess any special scientific culture.

The subject is treated experimentally throughout, and
I have endeavoured so to place each experiment before
the reader, that he should realise it as an actual operation.
My desire indeed has been to give distinct images of the
Carious phenomena of acoustics, and to cause them to be
seen mentally in their true relations.

I have been indebted to the kindness of some of my
English friends for a more or less complete examination of
the proof sheets of this work. To one celebrated (reran n,n
friend, who has given himself the trouble of reading the
proofs from beginning to end, my special thanks are due
and tendered.

There is a growing desire for scientific culture through-
out the civilised world. The feeling is natural, and, under
the circumstances, inevitable. For a power which in-
fluences so mightily the intellectual and material action of
the age, could not fail to arrest attention and challenge
examination. In our schools and universities a move-
ment in favour of science has begun which, no doubt,
will end in the recognition of its claims, both as a source
of knowledge and as a means of discipline. If by



X PREFACE.

showing, however inadequately, the features and the mien
of physical science to men of influence who derive their
culture from another source, this book should indirectly
aid those engaged in the movement referred to, it will
not have been written in vain.

Four years ago a work was published by Professor
Helmholtz, entitled ' Die Lehre von den Tonempfindungen,'
to the scientific portion of which I have given considerable
attention. Copious references to it will be found in the
following pages ; but they fail to give an adequate idea of
the thoroughness and excellence of the work. To those
especially who wish to pursue the subject into its aesthetic
developments, the Third Part of the Tonempfindungen
cannot fail to be of the highest interest and use.

Finally, I have ventured to connect this book with the
name of a man, who, had he lived, would have been the
first to turn it to good account; who blended in his
own beautiful character the wisdom of mature years with
the spring-like freshness of a boy. When together indeed,
we were men and boys by turns. This union of life, love,
and wisdom rendered Richard Dawes a great educator of
the young, in which capacity, and to the incalculable
profit of the village children on whom his influence fell,
he nobly and beneficently spent his life.



The Illustrations of this work were for the most part
drawn for me by Mr. Becker, to whose ability as a
mechanician and to whose skill as a draughtsman I am
continually indebted. The wood engravings were executed
by Mr. Branston.



CONTENTS.



LECTUKE I.

The Nerves and Sensation Production and Propagation of Sonorous
Motion Experiments on Sounding Bodies placed in Vacuo Action of
Hydrogen on the Voice Propagation of Sound through Air of varying
density Reflection of Sound Echoes Refraction of Sound Inflection
of Sound; Case of Erith Village and Church Influence of Temperature
on Velocity Influence of Density and Elasticity Newton's calculation
of Velocity Thermal changes produced by the Sonorous "Wave Laplace's
correction of Newton's Formula Ratio of specific Heats at constant
pressure and at constant volume deduced from velocities of Sound
Mechanical equivalent of Heat deduced from this ratio Inference that
Atmospheric Air possesses no sensible power to radiate Heat Velocity of
Sound in different Gases Velocity in Liquids and Solids Influence of
Molecular Structure on the velocity of Sound . . . PAGE 1

SUMMARY OF LECTURE 1 44

LECTURE II.

Physical distinction between Noise and Music A Musical Tone produced
by periodic, Noise produced by unperiodic, Impulses Production of
Musical Sounds by Taps Production of Musical Sounds by Puffs
Definition of Pitch in Music Vibrations of a Tuning-fork ; their graphic
representation on Smoked Glass Optical expression of the Vibrations
of a Tuning-fork Description of the Syren Limits of the Ear ; highest
and deepest Tones Rapidity of Vibration determined by the Syren
Determination of the Lengths of Sonorous Waves Wave-lengths of the
Human Voice in Man and Woman Transmission of Musical Sounds
through Liquids and Solids 48

SUMMARY OF LECTURE II. .... ... 83



LECTURE III.

Vibrations of Strings How employed in Music Influence of Sound-Boards
Laws of Vibrating Strings Illustrations on a large scale Combina-



Xll CONTENTS.

tion of Direct and Keflected Pulses Stationary and Progressive Waves
Nodes and Ventral Segments Application of results to the vibrations of
Musical Strings Experiments of M. Melde Strings set in vibration by
Tuning-forks Laws of Vibration thus demonstrated Harmonic Tones
of Strings Definitions of Timbre or Quality, of Overtones and Clang
Abolition of special Harmonics Conditions which affect the intensity of
the Harmonic Tones Optical examination of the Vibrations of a Piano-
wire .......... PAGE 86

SUMMARY OF LECTURE III ....... 125

LECTUEE IV.

Vibrations of a Eod fixed at both ends : its Subdivisions and corresponding
Overtones Vibrations of a Rod fixed at one end The Kaleidophone
Tho Iron Fiddle and Musical Box Vibrations of a Eod free at both
ends The Claquebois and Glass Harmonica Vibrations of a Tuning-
fork: its Subdivision and Overtones Vibrations of Square Plates
Chladni's discoveries Wheatstone's Analysis of the Vibrations of Plates
Chladni's Figures Vibrations of Discs and Bells Experiments of
Faraday and Strehlke ........ 128

SUMMARY OF LECTURE IV. . . . . . . . . 156

LECTUEE V.

Longitudinal Vibrations of a "Wire Eelative velocities of Sound in Brass
and Iron Longitudinal Vibrations of Eods fixed at one end Of Eods
free at both ends Divisions and Overtones of Eods vibrating longi-
tudinallyExamination of Vibrating Bars by Polarised Light Determi-
nation of Velocity in Solids Eesonance Vibrations of stopped Pipes :
their Divisions and Overtones Eelation of the Tones of stopped Pipes
to those of open Pipes Condition of Column of Air within a Sounding
Organ-pipe Eeeds and Eeed-pipes The Organ of Voice Overtones of
the Vocal Chords The Vowel Sounds Kundt's experiments New
methods of determining Velocity of Sound . . . . 159

SUMMARY OF LECTURE V ........ . 212



LECTUEE VI.

Sounding Flames Influence of the Tube surrounding the Flame Influence
of Size of Flame Harmonic Notes of Flames Effect of Uni sonant
Notes on Singing Flames Action of Sound on Naked Flames Experi-
ments with Fish-tail and Bat's-wing Burners Experiments on Tall
Flames Extraordinary delicacy of Flames as Acoustic Eeagents The
Vowel Flame Action of Conversational Tones upon Flames Action of
Musical Sounds on unignited Jets of Gas Constitution of Water Jets
Action of Musical Sounds on Water Jets A Liquid Vein may compete in
point of delicacy with the Ear . -;;-'/ . .. .. ,- .; . 217

SUMMARY OF LECTURK VI. . ', .' ? . . . -. - 252



CONTENTS. xiii

LECTUEE VII.

Law of Vibratory Motions in Water and Air Superposition of Vibrations
Interference and Coincidence of Sonorous Waves Destruction of Sound
by Sound Combined action of two Sounds nearly in unison with each
other Theory of Beats Optical Illustration of the principle of Inter-
ference Augmentation of Intensity by partial extinction of Vibrations
Eesultant Tones Conditions of their Production Experimental
Illustrations Difference Tones and Summation Tones Theories of
Young and Helmholtz PAGE 255

SlIMMAEY OF LECTURE VII. 284

LECTUKE VIII. ^

Combination of Musical Sounds The smaller the two Numbers which
express the Ratio of their Hates of Vibration, the more perfect is the
Harmony of two Sounds Notions of the Pythagoreans regarding
Musical Consonance Euler's theory of Consonance Physical Analysis
of the question Theory of Helmholtz Dissonance due to Beats Inter-
ference of Primary Tones and of Overtones Graphic representation of
Consonance and Dissonance Musical Chords The Diatonic Scale
Optical Illustration of Musical Intervals Lissajous' Figures Sympa-
thetic Vibrations Mechanism of Hearing Schultze's Bristles The
Otolithes Corti's Fibres Conclusion . 286




SOUND.



LECTUEE I.

THE NERVES AND SENSATION PRODUCTION AND PROPAGATION OF SONOROUS
MOTION EXPERIMENTS ON SOUNDING BODIES PLACED IN VACUO ACTION

OF HYDROGEN ON THE VOICE PROPAGATION OF SOUND THROUGH AIR OF

VARYING DENSITY REFLECTION OF SOUND ECHOES REFRACTION OF

SOUND INFLECTION OF SOUND ; CASE OF ERITH VILLAGE AND CHURCH

INFLUENCE OF TEMPERATURE ON VELOCITY INFLUENCE OF DENSITY

AND ELASTICITY NEWTON* S CALCULATION OF VELOCITY THERMAL CHANGES

PRODUCED BY THE SONOROUS "WAVE LAPLACE'S CORRECTION OF NEWTON* S
FORMULA KATIO OF SPECIFIC HEATS AT CONSTANT PRESSURE AND AT

CONSTANT VOLUME DEDUCED FROM VELOCITIES OF SOUND MECHANICAL

EQUIVALENT OF HEAT DEDUCED FROM THIS RATIO INFERENCE THAT AT-
MOSPHERIC AIR POSSESSES NO SENSIBLE POWER TO RADIATE HEAT

VELOCITY OF SOUND IN DIFFERENT GASES VELOCITY IN LIQUIDS AND
SOLIDS INFLUENCE OF MOLECULAR STRUCTURE ON THE VELOCITY OF
SOUND.

THE various nerves of the human body have their
origin in the brain, and the brain is the seat of sen-
sation. When you wound your finger, the nerves which
run from the finger to the brain convey intelligence of
the injury, and if these nerves be severed, however serious
the hurt may be, no pain is experienced. We have the
strongest reason for believing that what the nerves convey
to the brain is in all cases motion. It is the motion excited
by sugar in the nerves of taste which, transmitted to the
brain, produces the sensation of sweetness, while bitterness
is the result of the motion produced by aloes. It is



2 LECTURE I.

the motion excited in the olfactory nerves by the efflu-
vium of a rose, which announces itself in the brain as
the odour of the rose. It is the motion imparted by
the sunbeams to the optic nerve which, when it reaches
the brain, awakes the consciousness of light ; while a
similar motion imparted to other nerves resolves itself
into heat in the same wonderful organ.*

The motion here meant is not that of the nerve as a
whole ; it is the vibration, or tremor, of its molecules or
smallest particles.

Different nerves are appropriated to the transmission of
different kinds of molecular motion. The nerves of taste,
for example, are not competent to transmit the tremors of
light, nor is the optic nerve competent to transmit sonorous
vibration. For this latter a special nerve is necessary, which
passes from the brain into one of the cavities of the ear,
and there spreads out in a multitude of filaments. It is
the motion imparted to this, the auditory nerve, which,
in the brain, is translated into sound.

We have this day to examine how sonorous motion is
produced and propagated. Applying a flame to this small
collodion balloon, which contains a mixture of oxygen and
hydrogen, the gases explode, and every ear in this room is
conscious of a shock, to which the name of sound is given.
How was this shock transmitted from the balloon to your
organs of hearing ? Have our exploding gases shot the
air-particles against the auditory nerve as a gun shoots a
ball against a target ? No doubt, in the neighbourhood
of the balloon, there is to some extent a propulsion of
particles ; but air shooting through air comes speedily
to rest, and no particle of air from the vicinity of the
balloon reached the ear of any person here present. The

* The rapidity -with which an impression is transmitted through the
nerves, as first determined by Helmholtz and confirmed by Du Bois Raymond,
is 93 feet a second.




PRODUCTION AND PEO

process was this : When the flame^To'SSrecPfn'e mixed
gases they combined chemically, and their union was ac-
companied by the development of intense heat. The air
at this hot focus expanded suddenly, forcing the surround-
ing air violently away on all sides. This motion of the
air close to the balloon was rapidly imparted to that a
little further off, the air first set in motion coming at the
same time to rest. The air, at a little distance, passed its
motion on to the air at a greater distance, and came also
in its turn to rest. Thus each shell of air, if I may use
the term, surrounding the balloon, took up the motion of
the shell next preceding, and transmitted it to the next
succeeding shell, the motion being thus propagated as a
pulse or wave through the air.

In air at the freezing temperature this pulse is propa-
gated with a speed of 1,090 feet a second.

The motion of the pulse must not be confounded with
the motion of the particles which at any moment constitute
the pulse. For while the wave moves forward through
considerable distances, each particular particle of air makes
only a small excursion to and fro.

Fia. 1.




The process may be rudely represented by- the propaga-
tion of motion through a row of glass balls, such as are
employed in the game of solitaire. I place these balls
along a groove thus, fig. 1, each of them touching its



4 LECTURE I.

neighbours. Taking one of them in my hand, I urge it
against the end of the row. The motion thus imparted
to the first ball is delivered up to the second, the motion
of the second is delivered up to the third, the motion
of the third is imparted t9 the fourth; each ball, after
having given up its motion, returning itself to rest. The
last ball only of the row flies away. Thus is sound conveyed
from particle to particle through the air. The particles
which fill the cavity of the ear are finally driven against
the tympanic membrane, which is stretched across the
passage leading to the brain. This membrane, which
closes the 'drum' of the ear, is thrown into vibration,
its motion is transmitted to the ends of the auditory
nerve, and afterwards along the nerve to the brain, where
the vibrations are translated into sound. .How it is that
the motion of the nervous matter can thus excite the
consciousness of sound is a mystery which we cannot
fathom.

Let me endeavour to illustrate the propagation of sound
by another homely but useful illustration. I have here




five young assistants, A, B, c, D, and E, fig. 2, placed in a row,
one behind the other, each boy's hands resting against the
back of the boy in front of him. E is now foremost, and
A finishes the row behind. I suddenly push A ; A pushes



A SONOROUS WAVE. 5

B, and regains bis upright position ; B pushes c ; c pushes
D ; D pushes E ; each boy, after the transmission of the
push, becoming himself erect. E, having nobody in front,
is thrown forward. Had he been standing on the edge
of a precipice, he would have fallen over ; had he stood
in contact with a window, he would have broken the glass ;
had he been close to a drum-head, he would have shaken
the drum. We could thus transmit a push through a
row of a hundred boys, each particular boy, however, only
swaying to and fro. Thus, also, we send sound through
the air, and shake the drum of a distant ear, while each
particular particle of the air concerned in the transmission
of the pulse makes only a small oscillation.

Scientific education ought to teach us to see the in-
visible as well as the visible in nature ; to picture with
the eye of the mind those operations which entirely
elude the eye of the body ; to look at the very atoms of
matter in motion and at rest, and to follow them forth,
without ever once losing sight of them, into the world
of the senses, and see them there integrating themselves
in natural phenomena. With regard to the point now
under consideration, you will, I trust, endeavour to form
a definite image of a wave of sound. You ought to see
mentally the air particles when urged outwards by the
explosion of our balloon crowding closely together ; but
immediately behind this condensation you ought to see the
particles separated more widely apart. You ought, in short,
to be able to seize the conception that a sonorous wave con-
sists of two portions, in the one of which the air is more
dense, and in the other of which it is less dense than usual.
A condensation and a rarefaction, then, are the two con-
stituents of a wave of sound.*

Let us turn once more to our row of boys, for we have

* A sonorous wave will be more strictly defined in Lecture II.



H LECTUKE I.

not yet extracted from them all that they can teach us.
When I push A, he may yield languidly, and thus tardily
deliver up the motion to his neighbour B. B may do the
same to c, c to D, and D to E. In this way the motion
may be transmitted with comparative slowness along
the line. But A, when I push him, may, by a sharp
muscular effort and sudden recoil, deliver up promptly
his motion to B, and come himself to rest ; B may do the
same to c, c to D, and D to E, the motion being thus trans-
mitted rapidly along the line. Now this sharp muscular
effort and sudden recoil is analogous to the elasticity
of the air in the case of sound. In a wave of sound,
a lamina of air, when urged against its neighbour lamina,
delivers up its motion and recoils, in virtue of the elastic
force exerted between them ; and the more rapid this
delivery and recoil, or in other words the greater the
elasticity of the air, the greater is the velocity of the
sound.

But if air be thus necessary to the propagation of sound,
what must occur when a sonorous body, a ringing bell for
example, is placed in a space perfectly void of air ? Out of
that space the sound could never come. The hammer might
strike, but it would strike silently. A celebrated experiment
which proved this was made by a philosopher named Hawks-
bee, before the Royal Society in 1705.* He so fixed a bell
within the receiver of an air-pump, that he could ring the
bell when the receiver was exhausted. Before the air was
withdrawn the sound of the bell was heard within the re-
ceiver ; after the air was withdrawn the sound became so
faint as to be hardly perceptible. I have here an arrange-
ment which enables me to repeat, in a very perfect manner,
the experiment of Hawksbee. Within this jar, G G' ? fig. 3,
restingon the plate of an air-pump is a bell, B, associated with

* Philosophical Transactions, 1705.



BELL L\ VACUO.



Fro. 3.



clockwork.* I exhaust the jar as perfectly as possible, and
now, by means of a rod, rr', which passes air-tight through
the top of the vessel, I loose the detent which holds the ham-
mer. It strikes, and you see it striking, but only those close
to the bell can hear the sound. I now allow hydrogen gas,
which you know is fourteen
times lighter than air, to enter
the vessel. The sound of the
bell is not sensibly augmented
by the presence of this attenu-
ated gas, though the receiver
is now full of it.f By work-
ing the pump, the atmosphere
round the bell is rendered still
more attenuated. In this way
we obtain a vacuum more
perfect than that of Hawks-
bee, and this is important, for
it is the last traces of air that
are chiefly effective in this
experiment. You now see the
hammer pounding the bell,
but you hear no sound. Even
when I place my ear against
the exhausted receiver, I am
unable to hear the faintest tinkle. Observe also that
the bell is suspended by strings, for if it were allowed to.
rest upon the plate of the air-pump, the vibrations would
communicate themselves to the plate, and be transmitted

* A very effective instrument presented to the Royal Institution by Mr.
"Warren De la Rue.

t Leslie, I believe, was the first to notice this. Air, it may be stated,
reduced to the specific gravity of hydrogen, transmits the sound of the bell
vastly better than hydrogen. A whole atmosphere of this gas has no
sensible effect in restoring the sound of the bell, while the fifteenth of an
atmosphere of air renders its ringing very audible.




8 LECTUKE I.

to the air outside. All that I can hear by the most con-
centrated attention, with my ear placed against the receiver,
is a feeble thud, due to the transmission of the shock of
the hammer through the strings which support the bell.
I now permit air to enter the jar with as little noise as
possible. You immediately hear a feeble sound, which
grows louder as the air becomes more dense; and now
every person in this large assembly distinctly hears the
ringing of the bell.*

At great elevations in the atmosphere sound is sensibly
diminished in loudness. De Saussure thought the explosion
of a pistol at the summit of Mont Blanc to be about equal
to that of a common cracker below. I have several times
repeated this experiment : first, in default of anything
better, with a little tin cannon, the .torn remnants of
which are now before you, and afterwards with pistols.
What struck me was the absence of that density and
sharpness in the sound which characterise it at lower
elevations. The pistol-shot resembled the explosion of a
champagne bottle, but it was still loud. The withdrawal
of half an atmosphere does not very materially affect our
ringing bell, and air of the density found at the top of
Mont Blanc is still capable of powerfully affecting the
auditory nerve. That highly attenuated air is able to
convey sound of great intensity, is forcibly illustrated by
the explosion of meteorites at great elevations above the
earth. Here, however, the initial disturbance must be
exceedingly violent.

The motion of sound, like all other motion, is enfeebled
by its transference from a light body to a heavy one.
I remove the receiver which has hitherto covered our bell ;

* By directing the beam of an electric lamp on glass "bulbs filled with a
mixture of equal volumes of chlorine and hydrogen, I have caused the bulbs
to explode in vacuo and in air. The difference, though not so striking as I
at first expected, was peti ? ectly distinct.



EFFECT OF HYDROGEN UPON THE VOICE. 9

you hear how much more loudly it rings in the open air.
When the bell was covered the aerial vibrations were first
communicated to the heavy glass jar, and afterwards by
the jar to the air outside ; a great diminution of intensity
being the consequence. The action of hydrogen gas upon
the voice is an illustration of the same kind. The voice is
formed by urging air from the lungs through an organ
called the larynx. In its passage it is thrown into vibra-
tion by the vocal chords which thus generate sound. But
when I fill my lungs with hydrogen, and endeavour to
speak, the vocal chords impart their motion to the hydro-
gen, which transfers it to the outer air. By this trans-
ference from a light gas to a heavy one, the sound is
weakened in a remarkable degree.* The consequence is
very curious. You have already formed a notion of the
strength and quality of my voice. I now empty my lungs
of air, and inflate them with hydrogen from this gasholder.
I try to speak vigorously, but my voice has lost wonder-
fully in power, and changed wonderfully in quality. You
hear it, hollow, harsh, and unearthly: I cannot otherwise
describe it.

The intensity of a sound depends on the density of the
air in which the sound is generated, and not on that of the
air in which it is heard.f Supposing the summit of Mont
Blanc to be equally distant from the top of the Aiguille
Verte and the bridge at Chamouni; and supposing two
observers stationed, the one upon the bridge and the
other upon the Aiguille : the sound of a cannon fired on
Mont Blanc would reach both observers with the same in-
tensity, though in the one case the sound would pursue its
way through the rare air above, while in the other it would
descend through the denser air below. Again, let a

* It may be that the gas fails to throw the vocal chords into sufficiently
strong vibration. The laryngoscope might decide this question,
t Poisson Me'canique, vol. ii. p. 707.



10 LECTURE I.

straight line equal to that from the bridge of Chamouni
to the summit of Mont Blanc, be measured along the
earth's surface in the valley of Chamouni, and let two ob-
servers be stationed, the one on the summit and the other
at the end of the line ; the sound of a cannon fired on the
bridge would reach both observers with the same intensity,



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