SOUND
BY
JOHN TYNDALL, D.C.L., LL.D., F.R.S.
[Illustration]
NEW YORK P. F. COLLIER & SON MCMII 7
SCIENCE
TO THE MEMORY
OF
MY FRIEND RICHARD DAWES
LATE DEAN OF HEREFORD
THIS BOOK IS DEDICATED
J. T.
CONTENTS
CHAPTER I
The Nerves and Sensation—Production and Propagation of
Sonorous Motion—Experiments on Sounding Bodies placed
in Vacuo—Deadening of Sound by Hydrogen—Action of
Hydrogen on the Voice—Propagation of Sound through Air
of Varying Density—Reflection of Sound—Echoes—Refraction
of Sound—Diffraction of Sound; Case of Erith Village and
Church—Influence of Temperature on Velocity—Influence
of Density on 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. 31
SUMMARY OF CHAPTER I 77
CHAPTER 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 Siren—Limits of the
Ear; Highest and Deepest Tones—Rapidity of Vibration
Determined by the Siren—Determination of the Lengths
of Sonorous Waves—Wave-Lengths of the Voice in Man and
Woman—Transmission of Musical Sounds through Liquids and
Solids. 82
SUMMARY OF CHAPTER II 117
CHAPTER III
Vibration of Strings—How employed in Music—Influence of
Sound-Boards—Laws of Vibrating String—Combination of
Direct and Reflected Pulses—Stationary and Progressive
Waves—Nodes and Ventral Segments—Application of Results
to the Vibrations of Musical Strings—Experiments of
Melde—Springs set in Vibration by Tuning-Forks—Laws
of Vibration thus demonstrated—Harmonic Tones of
Strings—Definitions of Timbre or Quality, or Overtones
and Clang—Abolition of Special Harmonies—Conditions
which affect the Intensity of the Harmonic Tones—Optical
Examination of the Vibrations of a Piano-Wire 120
SUMMARY OF CHAPTER III 161
CHAPTER IV
Vibrations of a Rod fixed at Both Ends: its Subdivisions
and Corresponding Overtones—Vibrations of a Rod fixed
at One End—The Kaleidophone—The Iron Fiddle and Musical
Box—Vibrations of a Rod free at Both Ends—The Claque-bois
and Glass Harmonica—Vibrations of a Tuning-Fork:
its Subdivisions and Overtones—Vibrations of Square
Plates—Chladni’s Discoveries—Wheatstone’s Analysis of
the Vibrations of Plates—Chladni’s Figures—Vibrations of
Disks and Bells—Experiments of Faraday and Strehlke. 165
SUMMARY OF CHAPTER IV 196
CHAPTER V
Longitudinal Vibrations of a Wire—Relative Velocities of
Sound in Brass and Iron—Longitudinal Vibrations of Rods
fixed at One End—Of Rods free at Both Ends—Divisions and
Overtones of Rods vibrating longitudinally—Examination
of Vibrating Bars by Polarized Light—Determination of
Velocity of Sound in Solids—Resonance—Vibrations of
Stopped Pipes: their Divisions and Overtones—Relation
of the Tones of Stopped Pipes to those of Open
Pipes—Condition of Column of Air within a Sounding
Organ-Pipe—Reeds and Reed-Pipes—The Voice—Overtones of
the Vocal Chords—The Vowel Sounds—Kundt’s Experiments—New
Methods of determining the Velocity of Sound. 200
SUMMARY OF CHAPTER V 254
CHAPTER VI
Singing Flames—Influence of the Tube surrounding
the Flame—Influence of Size of Flame—Harmonic Notes
of Flames—Effect of Unisonant Notes on Singing
Flames—Action of Sound on Naked Flames—Experiments with
Fish-Tail and Bat’s-Wing Burners—Experiments on Tall
Flames—Extraordinary Delicacy of Flames as Acoustic
Reagents—The Vowel-Flame—Action of Conversational
Tones upon Flames—Action of Musical Sounds on
Smoke-Jets—Constitution of Water-Jets—Plateau’s Theory
of the Resolution of a Liquid Vein into Drops—Action of
Musical Sounds on Water-Jets—A Liquid Vein may compete in
Point of Delicacy with the Ear 260
SUMMARY OF CHAPTER VI 301
CHAPTER VII
_PART I_
RESEARCHES ON THE ACOUSTIC TRANSPARENCY OF THE ATMOSPHERE
IN RELATION TO THE QUESTION OF FOG-SIGNALLING
Introduction—Instruments and Observations—Contradictory
Results from the 19th of May to the 1st of July
inclusive—Solution of Contradictions—Aërial Reflection
and its Causes—Aërial Echoes—Acoustic Clouds—Experimental
Demonstration of Stoppage of Sound by Aërial Reflection
305
_PART II_
INVESTIGATION OF THE CAUSES WHICH HAVE HITHERTO BEEN
SUPPOSED EFFECTIVE IN PREVENTING THE TRANSMISSION OF
SOUND THROUGH THE ATMOSPHERE
Action of Hail and Rain—Action of Snow—Action of Fog;
Observations in London—Experiments on Artificial
Fogs—Observations on Fogs at the South Foreland—Action of
Wind—Atmospheric Selection—Influence of Sound-Shadow 341
SUMMARY OF CHAPTER VII 374
CHAPTER VIII
Law of Vibratory Motions in Water and
Air—Superposition of Vibrations—Interference 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 Interference—Augmentation of Intensity
by Partial Extinction of Vibrations—Resultant
Tones—Conditions of their Production—Experimental
Illustrations—Difference-Tones and
Summation-Tones—Theories of Young and Helmholtz 377
SUMMARY OF CHAPTER VIII 407
CHAPTER IX
Combination of Musical Sounds—The smaller the Two
Numbers which express the Ratio of their Rates of
Vibration, the more perfect is the Harmony of Two
Sounds—Notions of the Pythagoreans regarding Musical
Consonance—Euler’s Theory of Consonance—Theory of
Helmholtz—Dissonance due to Beats—Interference of Primary
Tones and of Overtones—Mechanism of Hearing—Schultze’s
Bristles—The Otoliths—Corti’s Fibres—Graphic
Representation of Consonance and Dissonance—Musical
Chords—The Diatonic Scale—Optical Illustration of
Musical Intervals—Lissajous’s Figures—Sympathetic
Vibrations—Various Modes of illustrating the Composition
of Vibrations 410
Summary of Chapter IX 450
APPENDIX I
ON THE INFLUENCE OF MUSICAL SOUNDS ON THE FLAME OF A JET OF
COAL-GAS. BY JOHN LE CONTE, M.D. 454
APPENDIX II
ON ACOUSTIC REVERSIBILITY 461
INDEX 471
ILLUSTRATION—FOG-SIREN _Frontispiece_
[Illustration: FOG-SIREN]
PREFACE TO THE THIRD EDITION
In preparing this new edition of “Sound,” I have carefully gone over
the last one; amended, as far as possible, its defects of style
and matter, and paid at the same time respectful attention to the
criticisms and suggestions which the former editions called forth.
The cases are few in which I have been content to reproduce what I
have _read_ of the works of acousticians. I have sought to make myself
experimentally familiar with the ground occupied; trying, in all cases,
to present the illustrations in the form and connection most suitable
for educational purposes.
Though bearing, it may be, an undue share of the imperfection which
cleaves to all human effort, the work has already found its way into
the literature of various nations of diverse intellectual standing.
Last year, for example, a new German edition was published “under the
special supervision” of Helmholtz and Wiedemann. That men so eminent,
and so overladen with official duties, should add to these the labor of
examining and correcting every proof-sheet of a work like this, shows
that they consider it to be what it was meant to be—a serious attempt
to improve the public knowledge of science. It is especially gratifying
to me to be thus assured that not in England alone has the book met a
public want, but also in that learned land to which I owe my scientific
education.
Before me, on the other hand, lie two volumes of foolscap size,
curiously stitched, and printed in characters the meaning of which I
am incompetent to penetrate. Here and there, however, I notice the
familiar figures of the former editions of “Sound.” For these volumes
I am indebted to Mr. John Fryer, of Shanghai, who, along with them,
favored me, a few weeks ago, with a letter from which the following is
an extract: “One day,” writes Mr. Fryer, “soon after the first copy
of your work on Sound reached Shanghai, I was reading it in my study,
when an intelligent official, named Hsii-chung-hu, noticed some of the
engravings and asked me to explain them to him. He became so deeply
interested in the subject of Acoustics that nothing would satisfy him
but to make a translation. Since, however, engineering and other works
were then considered to be of more practical importance by the higher
authorities, we agreed to translate your work during our leisure time
every evening, and publish it separately ourselves. Our translation,
however, when completed, and shown to the higher officials, so much
interested them, and pleased them, that they at once ordered it to be
published at the expense of the Government, and sold at cost price. The
price is four hundred and eighty copper cash per copy, or about one
shilling and eightpence. This will give you an idea of the cheapness of
native printing.”
Mr. Fryer adds that his Chinese friend had no difficulty in grasping
every idea in the book.
The new matter of greatest importance which has been introduced into
this edition is an account of an investigation which, during the past
two years, I have had the honor of conducting in connection with the
Elder Brethren of the Trinity House. Under the title “Researches on the
Acoustic Transparency of the Atmosphere, in Relation to the Question of
Fog-signalling,” the subject is treated in Chapter VII. of this volume.
It was only by Governmental appliances that such an investigation
could have been made; and it gives me pleasure to believe that not
only have the practical objects of the inquiry been secured, but that
a crowd of scientific errors, which for more than a century and a half
have surrounded this subject, have been removed, their place being
now taken by the sure and certain truth of Nature. In drawing up the
account of this laborious inquiry, I aimed at linking the observations
so together that they alone should offer a substantial demonstration of
the principles involved. Further labors enabled me to bring the whole
inquiry within the firm grasp of _experiment_; and thus to give it a
certainty which, without this final guarantee, it could scarcely have
enjoyed.
Immediately after the publication of the first brief abstract of the
investigation, it was subjected to criticism. To this I did not deem it
necessary to reply, believing that the grounds of it would disappear
in presence of the full account. The only opinion to which I thought
it right to defer was to some extent a private one, communicated to
me by Prof. Stokes. He considered that I had, in some cases, ascribed
too exclusive an influence to the mixed currents of aqueous vapor and
air, to the neglect of differences of temperature. That differences
of temperature, when they come into play, are an efficient cause of
acoustic opacity, I never doubted. In fact, aërial reflection arising
from this cause is, in the present inquiry, for the first time made
the subject of experimental demonstration. What the relative potency
of differences of temperature and differences due to aqueous vapor, in
the cases under consideration, may be, I do not venture to state; but
as both are active, I have, in Chapter VII., referred to them jointly
as concerned in the production of those “acoustic clouds” to which the
stoppage of sound in the atmosphere is for the most part due.
Subsequently, however, to the publication of the full investigation
another criticism appeared, to which, in consideration of its source,
I would willingly pay all respect and attention. In this criticism,
which reached me first through the columns of an American newspaper,
differences in the amounts of aqueous vapor, and differences of
temperature, are alike denied efficiency as causes of acoustic
opacity. At a meeting of the Philosophical Society of Washington the
emphatic opinion had, it was stated, been expressed that I was wrong
in ascribing the opacity of the atmosphere to its flocculence, the
really efficient cause being _refraction_. This view appeared to me so
obviously mistaken that I assumed, for a time, the incorrectness of the
newspaper account.
Recently, however, I have been favored with the “Report of the United
States Lighthouse Board for 1874,” in which the account just referred
to is corroborated. A brief reference to the Report will here suffice.
Major Elliott, the accomplished officer and gentleman referred to at
page 261, had published a record of his visit of inspection to this
country, in which he spoke, with a perfectly enlightened appreciation
of the facts, of the differences between our system of lighthouse
illumination and that of the United States. He also embodied in his
Report some account of the investigation on fog-signals, the initiation
of which he had witnessed, and indeed aided, at the South Foreland.
On this able Report of their own officer the Lighthouse Board at
Washington make the following remark: “Although this account is
interesting in itself and to the public generally, yet, being addressed
to the Lighthouse Board of the United States, it would tend to convey
the idea that the facts which it states were new to the Board, and that
the latter had obtained no results of a similar kind; while a reference
to the appendix to this Report[1] will show that the researches of our
Lighthouse Board have been much more extensive on this subject than
those of the Trinity House, and that the latter has established no
facts of practical importance which had not been previously observed
and used by the former.”
The “appendix” here referred to is from the pen of the venerable Prof.
Joseph Henry, chairman of the Lighthouse Board at Washington. To his
credit be it recorded that at a very early period in the history of
fog-signalling Prof. Henry reported in favor of Daboll’s trumpet,
though he was opposed by one of his colleagues on the ground that
“fog-signals were of little importance, since the mariner should know
his place by the character of his soundings.” In the appendix, he
records the various efforts made in the United States with a view to
the establishment of fog-signals. He describes experiments on bells,
and on the employment of reflectors to reinforce their sound. These,
though effectual close at hand, were found to be of no use at a
distance. He corrects current errors regarding steam-whistles, which
by some inventors were thought to act like ringing bells. He cites the
opinion of the Rev. Peter Ferguson, that sound is better heard in fog
than in clear air. This opinion is founded on observations of the noise
of locomotives; in reference to which it may be said that others have
drawn from similar experiments diametrically opposite conclusions. On
the authority of Captain Keeney he cites an occurrence, “in the first
part of which the captain was led to suppose that fog had a marked
influence in deadening sound, though in a subsequent part he came to
an opposite conclusion.” Prof. Henry also describes an experiment made
during a fog at Washington, in which he employed “a small bell rung by
clockwork, the apparatus being the part of a moderator lamp, intended
to give warning to the keepers when the supply of oil ceased. The
result of the experiment was, he affirms, contrary to the supposition
of absorption of the sound by the fog.” This conclusion is not founded
on comparative experiments, but on observations made in the fog alone;
for, adds Prof. Henry, “the change in the condition of the atmosphere,
as to temperature and the motion of the air, before the experiment
could be repeated in clear weather, rendered the result not entirely
satisfactory.”
This, I may say, is the only experiment on fog which I have found
recorded in the appendix.
In 1867 the steam-siren was mounted at Sandy Hook, and examined by
Prof. Henry. He compared its action with that of a Daboll trumpet,
employing for this purpose a stretched membrane covered with sand, and
placed at the small end of a tapering tube which concentrated the
sonorous motion upon the membrane. The siren proved most powerful. “At
a distance of 50, the trumpet produced a decided motion of the sand,
while the siren gave a similar result at a distance of 58.” Prof. Henry
also varied the pitch of the siren, and found that in association with
its trumpet 400 impulses per second yielded the maximum sound; while
the best result with the unaided siren was obtained when the impulses
were 360 a second. Experiments were also made on the influence of
pressure; from which it appeared that when the pressure varied from
100 lbs. to 20 lbs., the distance reached by the sound (as determined
by the vibrating membrane) varied only in the ratio of 61 to 51. Prof.
Henry also showed the sound of the fog-trumpet to be independent of
the material employed in its construction; and he furthermore observed
the decay of the sound when the angular distance from the axis of the
instrument was increased. Further observations were made by Prof. Henry
and his colleagues in August, 1873, and in August, and September,
1874. In the brief but interesting account of these experiments a
hypothetical element appears, which is absent from the record of the
earlier observations.
It is quite evident from the foregoing that, in regard to the question
of fog-signalling, the Lighthouse Board of Washington have not been
idle. Add to this the fact that their eminent chairman gives his
services gratuitously, conducting without fee or reward experiments and
observations of the character here revealed, and I think it will be
conceded that he not only deserves well of his own country, but also
sets his younger scientific contemporaries, both in his country and
ours, an example of high-minded devotion.
I was quite aware, in a general way, that labors like those now for the
first time made public had been conducted in the United States, and
this knowledge was not without influence upon my conduct. The first
instruments mounted at the South Foreland were of English manufacture;
and I, on various accounts, entertained a strong sympathy for their
able constructor, Mr. Holmes. From the outset, however, I resolved to
suppress such feelings, as well as all other extraneous considerations,
individual or national; and to aim at obtaining the best instruments,
irrespective of the country which produced them. In reporting,
accordingly, on the observations of May 19 and 20, 1873 (our first two
days at the South Foreland), these were my words to the Elder Brethren
of the Trinity House:
“In view of the reported performance of horns and whistles in other
places, the question arises whether those mounted at the South
Foreland, and to which the foregoing remarks refer, are of the best
possible description.... I think our first duty is to make ourselves
acquainted with the best instruments hitherto made, no matter where
made; and then, if home genius can transcend them, to give it all
encouragement. Great and unnecessary expense may be incurred, through
our not availing ourselves of the results of existing experience.
“I have always sympathized, and I shall always sympathize, with the
desire of the Elder Brethren to encourage the inventor who first
made the magneto-electric light available for lighthouse purposes. I
regard his aid and counsel as, in many respects, invaluable to the
corporation. But, however original he may be, our duty is to demand
that his genius shall be expended in making advances on that which
has been already achieved elsewhere. If the whistles and horns that
we heard on the 19th and 20th be the very best hitherto constructed,
my views have been already complied with; but if they be not—and I
am strongly inclined to think that they are not—then I would submit
that it behooves us to have the best, and to aim at making the South
Foreland, both as regards light and sound, a station not excelled by
any other in the world.”
On this score it gives me pleasure to say that I never had a difficulty
with the Elder Brethren. They agreed with me; and two powerful
steam-whistles, the one from Canada, the other from the United States,
together with a steam-siren—also an American instrument—were in due
time mounted at the South Foreland. It will be seen in Chapter VII.
that my strongest recommendation applies to an instrument for which we
are indebted to the United States.
In presence of these facts, it will hardly be assumed that I wish
to withhold from the Lighthouse Board of Washington any credit that
they may fairly claim. My desire is to be strictly just; and this
desire compels me to express the opinion that their Report fails to
establish the inordinate claim made in its first paragraph. It contains
observations, but contradictory observations; while as regards the
establishment of any principle which should reconcile the conflicting
results, it leaves our condition unimproved.
But I willingly turn aside from the discussion of “claims” to the
discussion of science. Inserted, as a kind of intrusive element,
into the Report of Prof. Henry, is a second Report by General Duane,
founded on an extensive series of observations made by him in 1870 and
1871. After stating with distinctness the points requiring decision,
the General makes the following remarks:
“Before giving the results of these experiments, some facts will be
stated which will explain the difficulties of determining the power of
a fog-signal.
“There are six steam fog-whistles on the coast of Maine: these have
been frequently heard at a distance of twenty miles, and as frequently
cannot be heard at the distance of two miles, and this with no
perceptible difference in the state of the atmosphere.
“The signal is often heard at a great distance in one direction, while
in another it will be scarcely audible at the distance of a mile. This
is not the effect of wind, as the signal is frequently heard much
further against the wind than with it.[2] For example, the whistle on
Cape Elizabeth can always be distinctly heard in Portland, a distance
of nine miles, during a heavy northeast snowstorm, the wind blowing a
gale directly from Portland toward the whistle.[3]
“The most perplexing difficulties, however, arise from the fact that
the signal often appears to be surrounded by a belt, varying in radius
from one mile to one mile and a half, from which the sound appears to
be entirely absent. Thus, in moving directly from a station the sound
is audible for the distance of a mile, is then lost for about the
same distance, after which it is again distinctly heard for a long
time. This action is common to all ear-signals, and has been at times
observed at all the stations, at one of which the signal is situated on
a bare rock twenty miles from the mainland, with no surrounding objects
to affect the sound.”
It is not necessary to assume here the existence of a “belt,” at some
distance from the station. The passage of an acoustic cloud over the
station itself would produce the observed phenomenon.
Passing over the record of many other valuable observations in the
Report of General Duane, I come to a few very important remarks which
have a direct bearing upon the present question:
“From an attentive observation,” writes the General, “during three
years, of the fog-signals on this coast, and from the reports received
from the captains and pilots of coasting vessels, I am convinced that,
in some conditions of the atmosphere, the most powerful signals will be
at times unreliable.[4]
“Now it frequently occurs that a signal which, under ordinary
circumstances, would be audible at the distance of fifteen miles,
cannot be heard from a vessel at the distance of a single mile. This is
probably due to the reflection mentioned by Humboldt.
“The temperature of the air over the land where the fog-signal is
located being very different from that over the sea, the sound, in
passing from the former to the latter, undergoes reflection at their
surface of contact. The correctness of this view is rendered more
probable by the fact that, when the sound is thus impeded in the
direction of the sea, it has been observed to be much stronger inland.
“Experiments and observation lead to the conclusion that these
anomalies in the penetration and direction of sound from fog-signals
are to be attributed mainly to the want of uniformity in the
surrounding atmosphere, and that snow, rain, and fog, and the direction
of the wind, have much less influence than has been generally supposed.”
The Report of General Duane is marked throughout by fidelity to facts,
rare sagacity, and soberness of speculation. The last three of the
paragraphs just quoted exhibit, in my opinion, the only approach to a
true explanation of the phenomena which the Washington Report reveals.
At this point, however, the eminent Chairman of the Lighthouse Board
strikes in with the following criticism:
“In the foregoing I differ entirely in opinion from General Duane as
to the cause of extinction of powerful sounds being due to the unequal
density of the atmosphere. The velocity of sound is not at all affected
by barometric pressure; but if the difference in pressure is caused by
a difference in heat, or by the expansive power of vapor mingled with
the air, a slight degree of obstruction of sound may be observed. But
this effect we think is entirely too minute to produce the results
noted by General Duane and Dr. Tyndall, while we shall find in the
action of currents above and below a true and efficient cause.”
I have already cited the remarkable observation of General Duane,
that with a snowstorm from the northeast blowing against the sound,
the signal at Cape Elizabeth is always heard at Portland, a distance
of nine miles. The observations at the South Foreland, where the
sound has-been proved to reach a distance of more than twelve miles
against the wind, backed by decisive experiments, reduce to certainty
the surmises of General Duane. It has, for example, been proved that
a couple of gas-flames placed in a chamber can, in a minute or two,
render its air so non-homogeneous as to cut a sound practically off;
while the same sound passes without sensible impediment through showers
of paper-scraps, seeds, bran, raindrops, and through fumes and fogs of
the densest description. The sound also passes through thick layers of
calico, silk, serge, flannel, baize, close felt, and through pads of
cotton-net impervious to the strongest light.
As long, indeed, as the air on which snow, hail, rain or fog is
suspended is homogeneous, so long will sound pass through the air,
sensibly heedless of the suspended matter.[5] This point is illustrated
upon a large scale by my own observations on the Mer de Glace, and by
those of General Duane, at Portland, which prove the snow-laden air
from the northeast to be a highly homogeneous medium. Prof. Henry thus
accounts for the fact that the northeast snow-wind renders the sound
of Cape Elizabeth audible at Portland: In the higher regions of the
atmosphere he places an ideal wind, blowing in a direction opposed to
the real one, which _always_ accompanies the latter, and which more
than neutralizes its action. In speculating thus he bases himself on
the reasoning of Prof. Stokes, according to which a sound-wave moving
against the wind is tilted upward. The upper, and opposing wind, is
invented for the purpose of tilting again the already lifted sound-wave
downward. Prof. Henry does not explain how the sound-wave recrosses
the hostile lower current, nor does he give any definite notion of the
conditions under which it can be shown that it will reach the observer.
This, so far as I know, is the only theoretic gleam cast by the
Washington Report on the conflicting results which have hitherto
rendered experiments on fog-signals so bewildering. I fear it is an
_ignis fatuus_, instead of a safe guiding light. Prof. Henry, however,
boldly applies the hypothesis in a variety of instances. But he dwells
with particular emphasis upon a case of non-reciprocity which he
considers absolutely fatal to my views regarding the flocculence of
the atmosphere. The observation was made on board the steamer “City
of Richmond,” during a thick fog in a night of 1872. “The vessel was
approaching Whitehead from the southwestward, when, at a distance of
about six miles from the station, the fog-signal, which is a 10-inch
steam-whistle, was distinctly perceived, and continued to be heard with
increasing intensity of sound until within about three miles, when
the sound suddenly ceased to be heard, and was not perceived again
until the vessel approached within a quarter of a mile of the station,
although from conclusive evidence, furnished by the keeper, it was
shown that the signal had been sounding during the whole time.”
But while the 10-inch shore-signal thus failed to make itself heard
at sea, a 6-inch whistle on board the steamer made itself heard on
shore. Prof. Henry thus turns this fact against me. “It is evident,”
he writes, “that this result could not be due to any mottled condition
or want of acoustic transparency in the atmosphere, since this would
absorb the sound equally in both directions.” Had the observation been
made in a still atmosphere, this argument would, at one time, have had
great force. But the atmosphere was not still, and a sufficient reason
for the observed non-reciprocity is to be found in the recorded fact
that the wind was blowing against the shore-signal, and in favor of the
ship-signal.
But the argument of Prof. Henry, on which he places his main reliance,
would be untenable, even had the air been still. By the very aërial
reflection which he practically ignores, reciprocity may be destroyed
in a calm atmosphere. In proof of this assertion I would refer him
to a short paper on “Acoustic Reversibility,” printed at the end of
this volume.[6] The most remarkable case of non-reciprocity on record,
and which, prior to the demonstration of the existence and power of
acoustic clouds, remained an insoluble enigma, is there shown to be
capable of satisfactory solution. These clouds explain perfectly the
“abnormal phenomena” of Prof. Henry. Aware of their existence, the
falling off and subsequent recovery of a signal-sound, as noticed by
him and General Duane, is no more a mystery than the interception of
the solar light by a common cloud, and its restoration after the cloud
has moved or melted away.
The clew to all the difficulties and anomalies of this question is to
be found in the aërial echoes, the significance of which has been
overlooked by General Duane, and misinterpreted by Prof. Henry. And
here a word might be said with regard to the injurious influence still
exercised by authority in science. The affirmations of the highest
authorities, that from clear air no sensible echo ever comes, were
so distinct that my mind for a time refused to entertain the idea.
Authority caused me for weeks to depart from the truth, and to seek
counsel among delusions. On the day our observations at the South
Foreland began I heard the echoes. They perplexed me. I heard them
again and again, and listened to the explanations offered by some
ingenious persons at the Foreland. They were an “ocean-echo”: this
is the very phraseology now used by Prof. Henry. They were echoes
“from the crests and slopes of the waves”: these are the words of the
hypothesis which he now espouses. Through a portion of the month of
May, through the whole of June, and through nearly the whole of July,
1873, I was occupied with these echoes; one of the phases of thought
then passed through, one of the solutions then weighed in the balance
and found wanting, being identical with that which Prof. Henry now
offers for acceptation.
But though it thus deflected me from the proper track, shall I say that
authority in science is injurious? Not without some qualification. It
is not only injurious, but deadly, when it cows the intellect into fear
of questioning it. But the authority which so merits our respect as to
compel us to test and overthrow all its supports, before accepting a
conclusion opposed to it, is not wholly noxious. On the contrary, the
disciplines it imposes may be in the highest degree salutary, though
they may end, as in the present case, in the ruin of authority. The
truth thus established is rendered firmer by our struggles to reach it.
I groped day after day, carrying this problem of aërial echoes in my
mind; to the weariness, I fear, of some of my colleagues who did not
know my object. The ships and boats afloat, the “slopes and crests of
the waves,” the visible clouds, the cliffs, the adjacent lighthouses,
the objects landward, were all in turn taken into account, and all in
turn rejected.
With regard to the particular notion which now finds favor with Prof.
Henry, it suggests the thought that his observations, notwithstanding
their apparent variety and extent, were really limited as regards the
weather. For did they, like ours, embrace weather of all kinds, it is
not likely that he would have ascribed to the sea-waves an action which
often reaches its maximum intensity when waves are entirely absent.
I will not multiply instances, but confine myself to the definite
statement that the echoes have often manifested an astonishing strength
when the sea was of glassy smoothness. On days when the echoes were
powerful, I have seen the southern cumuli mirrored in the waveless
ocean, in forms almost as definite as the clouds themselves. By no
possible application of the law of incidence and reflection could the
echoes from such a sea return to the shore; and if we accept for a
moment a statement which Prof. Henry seems to indorse, that sound-waves
of great intensity, when they impinge upon a solid or liquid surface,
do not obey the law of incidence and reflection, but “roll along the
surface like a cloud of smoke,” it only increases the difficulty. Such
a “cloud,” instead of returning to the coast of England, would, in our
case, have rolled toward the coast of France. Nothing that I could say
in addition could strengthen the case here presented. I will only add
one further remark. When the sun shines uniformly on a smooth sea, thus
producing a practically uniform distribution of the aërial currents to
which the echoes are due, the direction in which the trumpet-echoes
reach the shore is always that in which the axis of the instrument is
pointed. At Dungeness this was proved to be the case throughout an
arc of 210°—an impossible result, if the direction of reflection were
determined by that of the ocean waves.
Rightly interpreted and followed out, these aërial echoes lead to a
solution which penetrates and reconciles the phenomena from beginning
to end. On this point I would stake the issue of the whole inquiry,
and to this point I would, with special earnestness, direct the
attention of the Lighthouse Board of Washington. Let them prolong
their observations into calm weather: if their atmosphere resembles
ours—which I cannot doubt—then I affirm that they will infallibly
find the echoes strong on days when all thought of reflection “from
the crests and slopes of the waves” must be discarded. The echoes
afford the easiest access to the core of this question, and it is for
this reason that I dwell upon them thus emphatically. It requires
no refined skill or profound knowledge to master the conditions of
their production; and these once mastered, the Lighthouse Board of
Washington will find themselves in the real current of the phenomena,
outside of which—I say it with respect—they are now vainly speculating.
The acoustic deportment of the atmosphere in haze, fog, sleet, snow,
rain, and hail will be no longer a mystery; even those “abnormal
phenomena” which are now referred to an imaginary cause, or reserved
for future investigation, will be found to fall naturally into place,
as illustrations of a principle as simple as it is universal.
“With the instruments now at our disposal wisely established along
our coasts, I venture to think that the saving of property, in ten
years, will be an exceedingly large multiple of the outlay necessary
for the establishment of such signals. The saving of life appeals to
the higher motives of humanity.” Such were the words with which I
wound up my Report on Fog-Signals.[7] One year after their utterance,
the “Schiller” goes to pieces on the Scilly rocks. A single calamity
covers the predicted multiple, while the sea receives three hundred
and thirty-three victims. As regards the establishment of fog-signals,
energy has been hitherto paralyzed by their reputed uncertainty. We
now know both the reason and the range of their variations; and such
knowledge places it within our power to prevent disasters like the
recent one. The inefficiency of bells, which caused their exclusion
from our inquiry, was sadly illustrated in the case of the “Schiller.”
JOHN TYNDALL.
ROYAL INSTITUTION, _June, 1875_.
PREFACE TO THE FIRST EDITION
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 endeavored
so to place each experiment before the reader that he should realize it
as an actual operation. My desire, indeed, has been to give distinct
images of the various 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 my celebrated German friend Clausius, who has given himself the
trouble of reading the proofs from beginning to end, my especial thanks
are due and tendered.
There is a growing desire for scientific culture throughout the
civilized world. The feeling is natural, and, under the circumstances,
inevitable. For a power which influences 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 movement
in favor 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 showing, however inadequately, the methods
and results of physical science to men of influence, who derive their
culture from another source, this book should indirectly aid in
promoting the movement referred to, it will not have been written in
vain.
SOUND
CHAPTER I
The Nerves and Sensation—Production and Propagation of
Sonorous Motion—Experiments on Sounding Bodies placed
in Vacuo—Deadening of Sound by Hydrogen—Action of
Hydrogen on the Voice—Propagation of Sound through Air
of Varying Density—Reflection of Sound—Echoes—Refraction
of Sound—Diffraction of Sound; Case of Erith Village and
Church—Influence of Temperature on Velocity—Influence of
Density on 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
§ 1. _Introduction: Character of Sonorous Motion. Experimental
Illustrations_
The various nerves of the human body have their origin in the brain,
which is the seat of sensation. When the finger is wounded, the
sensor nerves convey to the brain 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_. The motion
here meant is not, however, that of the nerve as a whole, but of its
molecules or smallest particles.[8]
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 vibrations. For these a special nerve
is necessary, which passes from the brain into one of the cavities of
the ear, and there divides into a multitude of filaments. It is the
motion imparted to this, the _auditory nerve_, which, in the brain, is
translated into sound.
Applying a flame to a 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, which we name a sound. How was this
shock transmitted from the balloon to our organs of hearing? Have the
exploding gases shot the air-particles against the auditory nerve as a
gun shoots a ball against a target? No doubt, in the neighborhood of
the balloon, there is to some extent a propulsion of particles; but no
particle of air from the vicinity of the balloon reached the ear of any
person here present. The process was this: When the flame touched the
mixed gases they combined chemically, and their union was accompanied
by the development of intense heat. The heated air expanded suddenly,
forcing the surrounding 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.
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.
[Illustration: FIG. 1.]
The process may be rudely represented by the propagation of motion
through a row of glass balls, such as are employed in the game of
_solitaire_. Placing the balls along a groove thus, Fig. 1, each of
them touching its neighbor, and urging one of them 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 to the fourth; each ball, after having
given up its motion, returning itself to rest. The last ball only of
the row flies away. In a similar way 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 from the external ear toward the
brain. This membrane, which closes outwardly the “drum” of the ear, is
thrown into vibration, its motion is transmitted to the ends of the
auditory nerve, and afterward along that 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 the human mind cannot fathom.
[Illustration: FIG. 2.]
The propagation of sound may be illustrated 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 B, and
regains his 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
drumhead, 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.
But we have not yet extracted from our row of boys all that they can
teach us. When A is pushed he may yield languidly, and thus tardily
deliver up the motion to his neighbor B. B may do the same to C, C
to D, and D to E. In this way the motion might be transmitted with
comparative slowness along the line. But A, when pushed, 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 transmitted 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 neighbor 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.
[Illustration: FIG. 3.]
A very instructive mode of illustrating the transmission of a
sound-pulse is furnished by the apparatus represented in Fig. 3,
devised by my assistant, Mr. Cottrell. It consists of a series of
wooden balls separated from each other by spiral springs. On striking
the knob A, a rod attached to it impinges upon the first ball B, which
transmits its motion to C, thence it passes to E, and so on through
the entire series. The arrival at D is announced by the shock of the
terminal ball against the wood, or, if we wish, by the ringing of a
bell. Here the elasticity of the air is represented by that of the
springs. The pulse may be rendered slow enough to be followed by the
eye.
Scientific education ought to teach us to see the invisible as well
as the visible in nature, to picture with the vision of the mind
those operations which entirely elude bodily vision; 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, we must endeavor to form
a definite image of a wave of sound. We ought to see mentally the
air-particles, when urged outward by the explosion of our balloon,
crowding closely together; but immediately behind this condensation we
ought to see the particles separated more widely apart. We must, in
short, to be able to seize the conception that a sonorous wave consists
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 constituents of a wave of sound. This
conception shall be rendered more complete in our next lecture.
§ 2. _Experiments in Vacuo, in Hydrogen, and on Mountains_
[Illustration: FIG. 4.]
That air is thus necessary to the propagation of sound was proved by a
celebrated experiment made before the Royal Society, by a philosopher
named Hawksbee, in 1705.[9] 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 receiver; after the air was withdrawn the sound became
so faint as to be hardly perceptible. An arrangement is before you
which enables us to repeat in a very perfect manner the experiment of
Hawksbee. Within this jar, G G′, Fig. 4, resting on the plate of an
air-pump is a bell, B, associated with clockwork.[10] After the jar
has been exhausted as perfectly as possible, I release, by means of a
rod, _r r′_, which passes air-tight through the top of the vessel, the
detent which holds the hammer. It strikes, and you see it striking,
but only those close to the bell can hear the sound. Hydrogen gas,
which you know is fourteen times lighter than air, is now allowed
to enter the vessel. The sound of the bell is not augmented by the
presence of this attenuated gas, though the receiver is now full of
it. By working the pump, the atmosphere round the bell is rendered
still more attenuated. In this way we obtain a vacuum more perfect than
that of Hawksbee, 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 the ear is
placed against the exhausted receiver not the faintest tinkle is heard.
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 be
communicated to the plate, and thence transmitted to the air outside.
Permitting the 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, until finally every person in this large assembly
distinctly hears the ringing of the bell.[11]
Sir John Leslie found hydrogen singularly incompetent to act as the
vehicle of the sound of a bell rung in the gas. More than this, he
emptied a receiver like that before you of half its air, and plainly
heard the ringing of the bell. On permitting hydrogen to enter the
half-filled receiver until it was wholly filled, the sound sank
until it was scarcely audible. This result remained an enigma until
it received a simple and satisfactory explanation at the hands of
Prof. Stokes. When a common pendulum oscillates it tends to form a
condensation in front and a rarefaction behind. But it is only _a
tendency_; the motion is so slow, and the air is so elastic, that
it moves away in front before it is sensibly condensed, and fills
the space behind before it can become sensibly dilated. Hence waves
or pulses are not generated by the pendulum. It requires a certain
sharpness of shock to produce the condensation and rarefaction which
constitute a wave of sound in air.
The more elastic and mobile the gas, the more able will it be to move
away in front and to fill the space behind, and thus to oppose the
formation of rarefactions and condensations by a vibrating body. Now
hydrogen is much more mobile than air; and hence the production of
sonorous waves in it is attended with greater difficulty than in air. A
rate of vibration quite competent to produce sound-waves in the one may
be wholly incompetent to produce them in the other. Both calculation
and observation prove the correctness of this explanation, to which we
shall again refer.
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 afterward with pistols. What struck me was the
absence of that density and sharpness in the sound which characterize
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 elevations where the tenuity of
the atmosphere must be almost infinite. Here, however, the initial
disturbance must be exceedingly great.
The motion of sound, like all other motion, is enfeebled by its
transference from a light body to a heavy one. When the receiver
which has hitherto covered our bell is removed you hear how much
more loudly it rings in the open air. When the bell was covered the
aërial vibrations were first communicated to the heavy glass jar,
and afterward 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, where
it is thrown into vibration by the _vocal chords_ which thus generate
sound. But when the lungs are filled with hydrogen, the vocal chords
on speaking produce a vibratory motion in the hydrogen, which then
transfers the motion to the outer air. By this transference from a
light gas to a heavy one the voice is so weakened as to become a mere
squeak.[12]
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.[13] 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 report of a cannon fired on Mont Blanc
would reach both observers with the same intensity, though in the one
case the sound would pursue its way through the rare air above, while
in the other it would descend though the denser air below. Again, let a
straight line equal to that from the bridge at Chamouni to the summit
of Mont Blanc be measured along the earth’s surface in the valley of
Chamouni, and let two observers be stationed, the one on the summit and
the other at the end of the line: the report of a cannon fired on the
bridge would reach both observers with the same intensity, though in
the one case the sound would be propagated through the dense air of the
valley, and in the other case would ascend through the rarer air of the
mountain. Finally, charge two cannon equally, and fire one of them at
Chamouni and the other at the top of Mont Blanc: the one fired in the
heavy air below may be heard above, while the one fired in the light
air above is unheard below.
§ 3. _Intensity of Sound. Law of Inverse Squares_
In the case of our exploding balloon the wave of sound expands on all
sides, the motion produced by the explosion being thus diffused over a
continually augmenting mass of air. It is perfectly manifest that this
cannot occur without an enfeeblement of the motion. Take the case of a
thin shell of air with a radius of one foot, reckoned from the centre
of explosion. A shell of air of the same thickness, but of two feet
radius, will contain four times the quantity of matter; if its radius
be three feet, it will contain nine times the quantity of matter; if
four feet, it will contain sixteen times the quantity of matter, and so
on. Thus the quantity of matter set in motion _augments_ as the square
of the distance from the centre of explosion. The intensity or loudness
of sound _diminishes_ in the same proportion. We express this law by
saying that the intensity of the sound _varies inversely as the square
of the distance_.
Let us look at the matter in another light. The mechanical effect of a
ball striking a target depends on two things—the weight of the ball,
and the velocity with which it moves. The effect is proportional to the
weight simply; but it is proportional to the square of the velocity.
The proof of this is easy, but it belongs to ordinary mechanics rather
than to our present subject. Now what is true of the cannon-ball
striking a target is also true of an air-particle striking the tympanum
of the ear. Fix your attention upon a particle of air as the sound-wave
passes over it; it is urged from its position of rest toward a neighbor
particle, first with an accelerated motion, and then with a retarded
one. The force which first urges it is opposed by the resistance of
the air, which finally stops the particle and causes it to recoil. At
a certain point of its excursion the velocity of the particle is its
maximum. _The intensity of the sound is proportional to the square of
this maximum velocity._
The distance through which the air-particle moves to and fro, when the
sound-wave passes it, is called the _amplitude_ of the vibration. The
intensity of the sound is proportional to the square of the amplitude.
§ 4. _Confinement of Sound-waves in Tubes_
This weakening of the sound, according to the law of inverse squares,
would not take place if the sound-wave were so confined as to prevent
its lateral diffusion. By sending it through a tube with a smooth
interior surface we accomplish this, and the wave thus confined
may be transmitted to great distances with very little diminution
of intensity. Into one end of this tin tube, fifteen feet long, I
whisper in a manner quite inaudible to the people nearest to me,
but a listener at the other end hears me distinctly. If a watch be
placed at one end of the tube, a person at the other end hears the
ticks, though nobody else does. At the distant end of the tube is
now placed a lighted candle, _c_, Fig. 5. When the hands are clapped
at this end, the flame instantly ducks down at the other. It is not
quite extinguished, but it is forcibly depressed. When two books, B
B′, Fig. 5, are clapped together, the candle is blown out.[14] You may
here observe, in a rough way, the speed with which the sound-wave is
propagated. The instant the clap is heard the flame is extinguished. I
do not say that the time required by the sound to travel this tube is
immeasurably short, but simply that the interval is too short for your
senses to appreciate it.
[Illustration: FIG. 5.]
That it is a _pulse_ and not a _puff_ of air is proved by filling one
end of the tube with the smoke of brown paper. On clapping the books
together no trace of this smoke is ejected from the other end. The
pulse has passed through both smoke and air without carrying either of
them along with it.
An effective mode of throwing the propagation of a pulse through air
has been devised by my assistant. The two ends of a tin tube fifteen
feet long are stopped by sheet India-rubber stretched across them.
At one end, _e_, a hammer with a spring handle rests against the
India-rubber; at the other end is an arrangement for the striking
of a bell, _c_. Drawing back the hammer _e_ to a distance measured
on the graduated circle and liberating it, the generated pulse is
propagated through the tube, strikes the other end, drives away the
cork termination _a_ of the lever _a b_, and causes the hammer _b_ to
strike the bell. The rapidity of propagation is well illustrated here.
When hydrogen (sent through the India-rubber tube H) is substituted for
air the bell does not ring.
[Illustration: FIG. 6.]
The celebrated French philosopher, Biot, observed the transmission
of sound through the empty water-pipes of Paris, and found that he
could hold a conversation in a low voice through an iron tube 3,120
feet in length. The lowest possible whisper, indeed, could be heard at
this distance, while the firing of a pistol into one end of the tube
quenched a lighted candle at the other.
§ 5. _The Reflection of Sound. Resemblances to Light_
The action of sound thus illustrated is exactly the same as that of
light and radiant heat. They, like sound, are wave-motions. Like
sound they diffuse themselves in space, diminishing in intensity
according to the same law. Like sound also, light and radiant heat,
when sent through a tube with a reflecting interior surface, may be
conveyed to great distances with comparatively little loss. In fact,
every experiment on the reflection of light has its analogy in the
reflection of sound. On yonder gallery stands an electric lamp, placed
close to the clock of this lecture-room. An assistant in the gallery
ignites the lamp, and directs its powerful beam upon a mirror placed
here behind the lecture-table. By the act of reflection the divergent
beam is converted into this splendid luminous cone traced out upon
the dust of the room. The point of convergence being marked and the
lamp extinguished, I place my ear at that point. Here every sound-wave
sent forth by the clock and reflected by the mirror is gathered up,
and the ticks are heard as if they came, not from the clock, but from
the mirror. Let us stop the clock, and place a watch _w_, Fig. 7, at
the place occupied a moment ago by the electric light. At this great
distance the ticking of the watch is distinctly heard. The hearing is
much aided by introducing the end _f_ of a glass funnel into the ear,
the funnel here acting the part of an ear-trumpet. We know, moreover,
that in optics the positions of a body and of its image are reversible.
When a candle is placed at this lower focus, you see its image on the
gallery above, and I have only to turn the mirror on its stand to make
the image of the flame fall upon any one of the row of persons who
occupy the front seat in the gallery. Removing the candle, and putting
the watch, _w_, Fig. 8, in its place, the person on whom the light
falls distinctly hears the sound. When the ear is assisted by the glass
funnel, the reflected ticks of the clock in our first experiment are
so powerful as to suggest the idea of something pounding against the
tympanum, while the direct ticks are scarcely if at all, heard.
[Illustration: FIG. 7.]
[Illustration: FIG. 8.]
One of these two parabolic mirrors, _n n′_, Fig. 9, is placed upon
the table, the other, _m m′_, being drawn up to the ceiling of this
theatre; they are five-and-twenty feet apart. When the carbon-points
of the electric light are placed in the focus _a_ of the lower mirror
and ignited, a fine luminous cylinder rises like a pillar to the upper
mirror, which brings the parallel beam to a focus. At that focus
is seen a spot of sunlike brilliancy, due to the reflection of the
light from the surface of a watch, _w_, there suspended. The watch
is ticking, but in my present position I do not hear it. At this
lower focus, _a_, however, we have the energy of every sonorous wave
converged. Placing the ear at _a_, the ticking is as audible as if the
watch were at hand; the sound, as in the former case, appearing to
proceed, not from the watch itself, but from the lower mirror.[15]
[Illustration: FIG. 9.]
Curved roofs and ceilings and bellying sails act as mirrors upon
sound. In our old laboratory, for example, the singing of a kettle
seemed, in certain positions, to come, not from the fire on which it
was placed, but from the ceiling. Inconvenient secrets have been thus
revealed, an instance of which has been cited by Sir John Herschel.[16]
In one of the cathedrals in Sicily the confessional was so placed that
the whispers of the penitents were reflected by the curved roof, and
brought to a focus at a distant part of the edifice. The focus was
discovered by accident, and for some time the person who discovered
it took pleasure in hearing, and in bringing his friends to hear,
utterances intended for the priest alone. One day, it is said, his own
wife occupied the penitential stool, and both he and his friends were
thus made acquainted with secrets which were the reverse of amusing to
one of the party.
When a sufficient interval exists between a direct and a reflected
sound, we hear the latter as an _echo_.
Sound, like light, may be reflected several times in succession, and,
as the reflected light under these circumstances becomes gradually
feebler to the eye, so the successive echoes become gradually feebler
to the ear. In mountain regions this repetition and decay of sound
produce wonderful and pleasing effects. Visitors to Killarney will
remember the fine echo in the Gap of Dunloe. When a trumpet is sounded
in the proper place in the Gap, the sonorous waves reach the ear in
succession after one, two, three, or more reflections from the adjacent
cliffs, and thus die away in the sweetest cadences. There is a deep
_cul-de-sac_, called the Ochsenthal, formed by the great cliffs of the
Engelhörner, near Rosenlaui, in Switzerland, where the echoes warble in
a wonderful manner.
The sound of the Alpine horn, echoed from the rocks of the Wetterhorn
or the Jungfrau, is in the first instance heard roughly. But by
successive reflections the notes are rendered more soft and flute-like,
the gradual diminution of intensity giving the impression that the
source of sound is retreating further and further into the solitudes of
ice and snow. The repetition of echoes is also in part due to the fact
that the reflecting surfaces are at different distances from the hearer.
In large, unfurnished rooms the mixture of direct and reflected sound
sometimes produces very curious effects. Standing, for example, in the
gallery of the Bourse at Paris, you hear the confused vociferation of
the excited multitude below. You see all the motions—of their lips as
well as of their hands and arms. You know they are speaking—often,
indeed, with vehemence—but what they say you know not. The voices mix
with their echoes into a chaos of noise, out of which no intelligible
utterance can emerge. The echoes of a room are materially damped by its
furniture. The presence of an audience may also render intelligible
speech possible where, without an audience, the definition of the
direct voice is destroyed by its echoes. On the 16th of May, 1865,
having to lecture in the Senate House of the University of Cambridge,
I first made some experiments as to the loudness of voice necessary
to fill the room, and was dismayed to find that a friend, placed at a
distant part of the hall, could not follow me because of the echoes.
The assembled audience, however, so quenched the sonorous waves that
the echoes were practically absent, and my voice was plainly heard in
all parts of the Senate House.
Sounds are also said to be reflected from the clouds. Arago reports
that, when the sky is clear, the report of a cannon on an open plain
is short and sharp, while a cloud is sufficient to produce an echo
like the rolling of distant thunder. The subject of aërial echoes will
be subsequently treated at length, when it will be shown that Arago’s
conclusion requires correction.
Sir John Herschel, in his excellent article “Sound,” In the
“Encyclopædia Metropolitana,” has collected with others the following
instances of echoes. An echo in Woodstock Park repeats seventeen
syllables by day and twenty by night; one, on the banks of the Lago del
Lupo, above the fall of Terni, repeats fifteen. The tick of a watch may
be heard from one end of the abbey church of St. Albans to the other.
In Gloucester Cathedral, a gallery of an octagonal form conveys a
whisper seventy-five feet across the nave. In the whispering-gallery of
St. Paul’s, the faintest sound is conveyed from one side to the other
of the dome, but is not heard at any intermediate point. At Carisbrook
Castle, in the Isle of Wight, is a well two hundred and ten feet deep
and twelve wide. The interior is lined by smooth masonry; when a pin
is dropped into the well it is distinctly heard to strike the water.
Shouting or coughing into this well produces a resonant ring of some
duration.[17]
§ 6. _Refraction of Sound_
[Illustration: FIG. 10.]
Another important analogy between sound and light has been established
by M. Sondhauss.[18] When a large lens is placed in front of our
lamp, the lens compels the rays of light that fall upon it to deviate
from their direct and divergent course, and to form a convergent cone
behind it. This refraction of the luminous beam is a consequence of
the retardation suffered by the light in passing through the glass.
Sound may be similarly refracted by causing it to pass through a lens
which retards its motion. Such a lens is formed when we fill a thin
balloon with some gas heavier than air. A collodion balloon, B, Fig.
10, filled with carbonic-acid gas, the envelope being so thin as to
yield readily to the pulses which strike against it, answers the
purpose.[19] A watch, _w_, is hung up close to the lens, beyond which,
and at a distance of four or five feet from the lens, is placed the
ear, assisted by the glass funnel _f f′_. By moving the head about, a
position is soon discovered in which the ticking is particularly loud.
This, in fact, is the focus of the lens. If the ear be moved from this
focus the intensity of the sound falls; if, when the ear is at the
focus, the balloon be removed, the ticks are enfeebled; on replacing
the balloon their force is restored. The lens, in fact, enables us to
hear the ticks distinctly when they are perfectly inaudible to the
unaided ear.
[Illustration: FIG. 11.]
How a sound-wave is thus converged may be comprehended by reference to
Fig. 11. Let _m o n o″_ be a section of the sound-lens, and _a b_ a
portion of a sonorous wave approaching it from a distance. The middle
point, _o_, of the wave first touches the lens, and is first retarded
by it. By the time the ends _a_ and _b_, still moving through air,
reach the balloon, the middle point _o_, pursuing its way through the
heavier gas within, will have only reached _o′_. The wave is therefore
broken at _o_; and the direction of motion being at right angles to the
face of the wave, the two halves will encroach upon each other. This
convergence of the two halves of the wave is augmented on quitting the
lens. For when _o′_ has reached _o″_, the two ends _a_ and _b_ will
have pushed forward to a greater distance, say to _a′_ and _b′_. Soon
afterward the two halves of the wave will cross each other, or in other
words come to a focus, the air at the focus being agitated by the sum
of the motions of the two waves.[20]
§ 7. _Diffraction of Sound: illustrations offered by great Explosions_
When a long sea-roller meets an isolated rock in its passage, it rises
against the rock and embraces it all round. Facts of this nature caused
Newton to reject the undulatory theory of light. He contended that if
light were a product of wave-motion we could have no shadows, because
the waves of light would propagate themselves round opaque bodies as
a wave of water round a rock. It has been proved since his time that
the waves of light do bend round opaque bodies; but with that we have
nothing now to do. A sound-wave certainly bends thus round an obstacle,
though as it diffuses itself in the air at the back of the obstacle it
is enfeebled in power, the obstacle thus producing a partial _shadow_
of the sound. A railway train passing through cuttings and long
embankments exhibits great variations in the intensity of the sound.
The interposition of a hill in the Alps suffices to diminish materially
the sound of a cataract; it is able sensibly to extinguish the tinkle
of the cowbells. Still the sound-shadow is but partial, and the marker
at the rifle-butts never fails to hear the explosion, though he is well
protected from the ball. A striking example of this _diffraction_ of a
sonorous wave was exhibited at Erith after the tremendous explosion of
a powder magazine which occurred there in 1864. The village of Erith
was some miles distant from the magazine, but in nearly all cases the
windows were shattered; and it was noticeable that the windows turned
away from the origin of the explosion suffered almost as much as those
which faced it. Lead sashes were employed in Erith Church, and these,
being in some degree flexible, enabled the windows to yield to pressure
without much fracture of the glass. As the sound-wave reached the
church it separated right and left, and, for a moment, the edifice was
clasped by a girdle of intensely compressed air, every window in the
church, front and back, being bent _inward_. After compression, the air
within the church no doubt dilated, tending to restore the windows to
their first condition. The bending in of the windows, however, produced
but a small condensation of the whole mass of air within the church;
the recoil was therefore feeble in comparison with the pressure, and
insufficient to undo what the latter had accomplished.
§ 8. _Velocity of Sound: relation to Density and Elasticity of Air_
Two conditions determine the velocity of propagation of a sonorous
wave; namely, the elasticity and the density of the medium through
which the wave passes. The elasticity of air is measured by the
pressure which it sustains or can hold in equilibrium. At the sea-level
this pressure is equal to that of a stratum of mercury about thirty
inches high. At the summit of Mont Blanc the barometric column is not
much more than half this height; and, consequently, the elasticity of
the air upon the summit of the mountain is not much more than half what
it is at the sea-level.
If we could augment the elasticity of air, without at the same time
augmenting its density, we should augment the velocity of sound. Or,
if allowing the elasticity to remain constant we could diminish the
density, we should augment the velocity. Now, air in a closed vessel,
where it cannot expand, has its elasticity augmented by heat, while
its density remains unchanged. Through such heated air sound travels
more rapidly than through cold air. Again, air free to expand has its
density lessened by warming, its elasticity remaining the same, and
through such air sound travels more rapidly than through cold air. This
is the case with our atmosphere when heated by the sun.
The velocity of sound in air, _at the freezing temperature_, is 1,090
feet a second.
At all lower temperatures the velocity is less than this, and at all
higher temperatures it is greater. The late M. Wertheim has determined
the velocity of sound in air of different temperatures, and here are
some of his results:
Temperature of air Velocity of sound
0·5° centigrade 1,089 feet
2·10 ” 1,091 ”
8·5 ” 1,109 ”
12·0 ” 1,113 ”
26·6 ” 1,140 ”
At a temperature of half a degree above the freezing-point of water the
velocity is 1,089 feet a second; at a temperature of 26·6 degrees, it
is 1,140 feet a second, or a difference of 51 feet for 26 degrees; that
is to say, an augmentation of velocity of nearly two feet for every
single degree centigrade.
With the same elasticity the density of hydrogen gas is much less than
that of air, and the consequence is that the velocity of sound in
hydrogen far exceeds its velocity in air. The reverse holds good for
heavy carbonic-acid gas. If density and elasticity vary in the same
proportion, as the law of Boyle and Mariotte proves them to do in
air when the temperature is preserved constant, they neutralize each
other’s effects; hence, if the temperature were the same, the velocity
of sound upon the summits of the highest Alps would be the same as that
at the mouth of the Thames. But, inasmuch as the air above is colder
than that below, the actual velocity on the summits of the mountains
is less than that at the sea-level. To express this result in stricter
language, the velocity is _directly_ proportional to the square root
of the elasticity of the air; it is also _inversely_ proportional to
the square root of the density of the air. Consequently, as in air
of a constant temperature elasticity and density vary in the same
proportion, and act oppositely, the velocity of sound is not affected
by a change of density, if unaccompanied by a change of temperature.
There is no mistake more common than to suppose the velocity of sound
to be augmented by density. The mistake has arisen from a misconception
of the fact that in solids and liquids the velocity is greater than in
gases. But it is the higher elasticity of those bodies, _in relation to
their density_, that causes sound to pass rapidly through them. Other
things remaining the same, an augmentation of density always produces a
diminution of velocity. Were the elasticity of water, which is measured
by its compressibility, only equal to that of air, the velocity of
sound in water, instead of being more than quadruple the velocity in
air, would be only a small fraction of that velocity. Both density and
elasticity, then, must be always borne in mind; the velocity of sound
being determined by neither taken separately, but by the relation of
the one to the other. The effect of small density and high elasticity
is exemplified in an astonishing manner by the luminiferous ether,
which transmits the vibrations of light—not at the rate of so many
feet, but at the rate of nearly two hundred thousand miles a second.
Those who are unacquainted with the details of scientific investigation
have no idea of the amount of labor expended in the determination of
those numbers on which important calculations or inferences depend.
They have no idea of the patience shown by a Berzelius in determining
atomic weights; by a Regnault in determining coefficients of expansion;
or by a Joule in determining the mechanical equivalent of heat. There
is a morality brought to bear upon such matters which, in point of
severity, is probably without a parallel in any other domain of
intellectual action. Thus, as regards the determination of the velocity
of sound in air, hours might be filled with a simple statement of
the efforts made to establish it with precision. The question has
occupied the attention of experimenters in England, France, Germany,
Italy, and Holland. But to the French and Dutch philosophers we owe
the application of the last refinements of experimental skill to the
solution of the problem. They neutralized effectually the influence
of the wind; they took into account barometric pressure, temperature,
and hygrometric condition. Sounds were started at the same moment
from two distant stations, and thus caused to travel from station to
station through the self-same air. The distance between the stations
was determined by exact trigonometrical observations, and means were
devised for measuring with the utmost accuracy the time required by the
sound to pass from the one station to the other. This time, expressed
in seconds, divided into the distance expressed in feet, gave 1,090
feet per second as the velocity of sound through air at the temperature
of 0° centigrade.
The time required by light to travel over all terrestrial distances is
practically zero; and in the experiments just referred to the moment
of explosion was marked by the flash of a gun, the time occupied
by the sound in passing from station to station being the interval
observed between the appearance of the flash and the arrival of the
sound. The velocity of sound in air once established, it is plain that
we can apply it to the determination of distances. By observing, for
example, the interval between the appearance of a flash of lightning
and the arrival of the accompanying thunder-peal, we at once determine
the distance of the place of discharge. It is only when the interval
between the flash and peal is short that danger from lightning is to be
apprehended.
§ 9. _Theoretic Velocity calculated by Newton Laplace’s Correction_
We now come to one of the most delicate points in the whole theory
of sound. The velocity through air has been determined by direct
experiment; but knowing the elasticity and density of the air, it is
possible, without any experiment at all, to calculate the velocity with
which a sound-wave is transmitted through it. Sir Isaac Newton made
this calculation, and found the velocity at the freezing temperature
to be 916 feet a second. This is about one-sixth less than actual
observation had proved the velocity to be, and the most curious
suppositions were made to account for the discrepancy. Newton himself
threw out the conjecture that it was only in passing from particle to
particle of the air that sound required _time_ for its transmission;
that it moved instantaneously _through the particles themselves_.
He then supposed the line along which sound passes to be occupied
by air-particles for one-sixth of its extent, and thus he sought to
make good the missing velocity. The very art and ingenuity of this
assumption were sufficient to throw doubt on it; other theories were
therefore advanced, but the great French mathematician Laplace was the
first to completely solve the enigma. I shall now endeavor to make you
thoroughly acquainted with his solution.
[Illustration: FIG. 12.]
Into this strong cylinder of glass, T U, Fig. 12, which is accurately
bored, and quite smooth within, fits an air-tight piston. By pushing
the piston down, I condense the air beneath it, heat being at the same
time developed. A scrap of amadou attached to the bottom of the piston
is ignited by the heat generated by compression. If a bit of cotton
wool dipped into bisulphide of carbon be attached to the piston, when
the latter is forced down, a flash of light, due to the ignition of
the bisulphide of carbon vapor, is observed within the tube. It is
thus proved that when air is compressed heat is generated. By another
experiment it may be shown that when air is rarefied cold is developed.
This brass box contains a quantity of condensed air. I open the cock,
and permit the air to discharge itself against a suitable thermometer;
the sinking of the instrument immediately declares the chilling of the
air.
All that you have heard regarding the transmission of a sonorous
pulse through air is, I trust, still fresh in your minds. As the
pulse advances it squeezes the particles of air together, and two
results follow from this compression. First, its elasticity is
augmented through the mere augmentation of its density. Secondly, its
elasticity is augmented by the heat of compression. It was the change
of elasticity which resulted from a change of density that Newton took
into account, and he entirely overlooked the augmentation of elasticity
due to the second cause just mentioned. Over and above, then, the
elasticity involved in Newton’s calculation, we have an additional
elasticity due to changes of temperature produced by the sound-wave
itself. When both are taken into account, the calculated and the
observed velocities agree perfectly.
But here, without due caution, we may fall into the gravest error. In
fact, in dealing with Nature, the mind must be on the alert to seize
all her conditions; otherwise we soon learn that our thoughts are not
in accordance with her facts. It is to be particularly noted that the
augmentation of velocity due to the changes of temperature produced by
the sonorous wave itself is totally different from the augmentation
arising from the heating of the general mass of the air. The _average_
temperature of the air is unchanged by the waves of sound. We cannot
have a condensed pulse without having a rarefied one associated with
it. But in the rarefaction, the temperature of the air is as much
lowered as it is raised in the condensation. Supposing, then, the
atmosphere parcelled out into such condensations and rarefactions, with
their respective temperatures, an extraneous sound passing through such
an atmosphere would be as much retarded in the latter as accelerated
in the former, and no variation of the average velocity could result
from such a distribution of temperature.
[Illustration: FIG. 13.]
Whence, then, does the augmentation pointed out by Laplace arise? I
would ask your best attention while I endeavor to make this knotty
point clear to you. If air be compressed it becomes smaller in volume;
if the pressure be diminished, the volume expands. The force which
resists compression, and which produces expansion, is the elastic
force of the air. Thus an external pressure squeezes the air-particles
together; their own elastic force holds them asunder, and the particles
are in equilibrium when these two forces are in equilibrium. Hence it
is that the external pressure is a measure of the elastic force. Let
the middle row of dots, Fig. 13, represent a series of air-particles
in a state of quiescence between the points _a_ and _x_. Then, because
of the elastic force exerted between the particles, if any one of them
be moved from its position of rest, the motion will be transmitted
through the entire series. Supposing the particle _a_ to be driven by
the prong of a tuning-fork, or some other vibrating body, toward _x_,
so as to be caused finally to occupy the position _a′_ in the lowest
row of particles: at the instant the excursion of _a_ commences, its
motion begins to be transmitted to _b_. In the next following moments
_b_ transmits the motion to _c_, _c_ to _d_, _d_ to _e_, and so on. So
that by the time _a_ has reached the position _a′_, the motion will
have been propagated to some point _o′_ of the line of particles more
or less distant from _a′_. The entire series of particles between _a′_
and _o′_ is then in a state of condensation. The distance _a′ o′_,
over which the motion has travelled during the excursion of _a_ to
_a′_, will depend upon the elastic force exerted between the particles.
Fix your attention on any two of the particles, say _a_ and _b_. The
elastic force between them may be figured as a spiral spring, and it
is plain that the more flaccid this spring the more sluggish would be
the communication of the motion from _a_ to _b_; while the stiffer
the spring the more prompt would be the communication of the motion.
What is true of _a_ and _b_ is true for every other pair of particles
between _a_ and _o_. Now the spring between every pair of these
particles _is suddenly stiffened_ by the heat developed along the line
of condensation, and hence the velocity of propagation is augmented
by this heat. Reverting to our old experiment with the row of boys,
it is as if, by the very act of pushing his neighbor, the muscular
rigidity of each boy’s arm was increased, thus enabling him to deliver
his push more promptly than he would have done without this increase
of rigidity. The _condensed_ portion of a sonorous wave is propagated
in the manner here described, and it is plain that the velocity of
propagation is augmented by the heat developed in the condensation.
Let us now turn our thoughts for a moment to the propagation of the
rarefaction. Supposing, as before, the middle row _a x_ to represent
the particles of air in equilibrium under the pressure of the
atmosphere, and suppose the particle _a_ to be suddenly drawn to the
right, so as to occupy the position _a″_ in the highest line of dots:
_a″_ is immediately followed by _b″_, _b″_ by _c″_, _c″_ by _d″_,
_d″_ by _e″_; and thus the rarefaction is propagated backward toward
_x″_, reaching a point _o″_ in the line of particles by the time _a_
has completed its motion to the right. Now, why does _b″_ follow
_a″_ when _a″_ is drawn away from it? Manifestly because the elastic
force exerted between _b″_ and _a″_ is less than that between _b″_
and _c″_. In fact, _b″_ will be driven after _a″_ by a force equal
to the difference of the two elasticities between _a″_ and _b″_ and
between _b″_ and _c″_. The same remark applies to the motion of _c″_
after _b″_, to that of _d″_ after _c″_, in fact, to the motion of each
succeeding particle when it follows its predecessor. The greater the
difference of elasticity on the two sides of any particle the more
promptly will it follow its predecessor. And here observe what the
_cold_ of rarefaction accomplishes. In addition to the diminution of
the elastic force between _a″_ and _b″_ by the withdrawal of _a″_ to a
greater distance, there is a further diminution due to the lowering of
the temperature. _The cold developed augments the difference of elastic
force on which the propagation of the rarefaction depends._ Thus we
see that because the heat developed in the condensation augments the
rapidity of the condensation, and because the cold developed in the
rarefaction augments the rapidity of the rarefaction, the sonorous
wave, which consists of a condensation and a rarefaction, must have its
velocity augmented by the heat _and the cold_ which it develops during
its own progress.
It is worth while fixing your attention here upon the fact that the
distance _a′ o′_, to which the motion has been propagated while _a_ is
moving to the position _a′_, may be vastly greater than that passed
over in the same time by the particle itself. The excursion of _a′_
may not be more than a small fraction of an inch, while the distance
to which the motion is transferred during the time required by _a′_
to perform this small excursion may be many feet, or even many yards.
If this point should not appear altogether plain to you now, it will
appear so by and by.
§ 10. _Ratio of Specific Heats of Air deduced from Velocity of Sound_
Having grasped this, even partially, I will ask you to accompany me to
a remote corner of the domain of physics, with the view, however, of
showing that remoteness does not imply discontinuity. Let a certain
quantity of air at a temperature of 0°, contained in a perfectly
inexpansible vessel, have its temperature raised 1°. Let the same
quantity of air, placed in a vessel which permits the air to expand
when it is heated—the pressure on the air being kept constant during
its expansion—also have its temperature raised 1°. The quantities
of heat employed in the two cases are different. The one quantity
expresses what is called the specific heat of air at constant volume;
the other the specific heat of air at constant pressure.[21] It is an
instance of the manner in which apparently unrelated natural phenomena
are bound together, that from the calculated and observed velocities
of sound in air we can deduce the ratio of these two specific heats.
Squaring Newton’s theoretic velocity and the observed velocity, and
dividing the greater square by the less, we obtain the ratio referred
to. Calling the specific heat at constant volume C^{v}, and that
at constant pressure C^{p}; calling, moreover, Newton’s calculated
velocity V, and the observed velocity V′, Laplace proved that—
C^{p} V′^{2}
————— = —————
C^{v} V^{2}
Inserting the values of V and V′ in this equation, and making the
calculation, we find—
C^{p}
————— = 1·42.
C^{v}
Thus, without knowing either the specific heat at constant volume or
at constant pressure, Laplace found the ratio of the greater of them
to the less to be 1·42. It is evident from the foregoing formulæ that
the calculated velocity of sound, multiplied by the square root of this
ratio, gives the observed velocity.
But there is one assumption connected with the determination of this
ratio, which must be here brought clearly forth. It is assumed that
the heat developed by compression _remains in the condensed portion of
the wave_, and applies itself there to augment the elasticity; that no
portion of it is lost by radiation. If air were a powerful radiator,
this assumption could not stand. The heat developed in the condensation
could not then remain in the condensation. It would radiate all
round, lodging itself for the most part in the chilled and rarefied
portion of the wave, which would be gifted with a proportionate power
of absorption. Hence the direct tendency of radiation would be to
equalize the temperatures of the different parts of the wave, and
thus to abolish the increase of velocity which called forth Laplace’s
correction.[22]
§ 11. _Mechanical Equivalent of Heat deduced from Velocity of Sound_
The question, then, of the correctness of this ratio involves the other
and apparently incongruous question, whether atmospheric air possesses
any sensible radiative power. If the ratio be correct, the practical
absence of radiative power on the part of air is demonstrated. How then
are we to ascertain whether the ratio is correct or not? By a process
of reasoning which illustrates still further how natural agencies are
intertwined. It was this ratio, looked at by a man of genius, named
Mayer, which helped him to a clearer and a grander conception of the
relation and interaction of the forces of inorganic and organic nature
than any philosopher up to his time had attained. Mayer was the first
to see that the excess 0·42 of the specific heat at constant pressure
over that at constant volume was the quantity of heat consumed in the
work performed by the expanding gas. Assuming the air to be confined
laterally and to expand in a vertical direction, in which direction it
would simply have to lift the weight of the atmosphere, he attempted
to calculate the precise amount of heat consumed in the raising of
this or any other weight. He thus sought to determine the “mechanical
equivalent” of heat. In the combination of his data his mind was clear,
but for the numerical correctness of these data he was obliged to rely
upon the experimenters of his age. Their results, though approximately
correct, were not so correct as the transcendent experimental ability
of Regnault, aided by the last refinements of constructive skill,
afterward made them. Without changing in the slightest degree the
method of his thought or the structure of his calculation, the simple
introduction of the exact numerical data into the formula of Mayer
brings out the true mechanical equivalent of heat.
But how are we able to speak thus confidently of the accuracy of this
equivalent? We are enabled to do so by the labors of an Englishman, who
worked at this subject contemporaneously with Mayer; and who, while
animated by the creative genius of his celebrated German brother,
enjoyed also the opportunity of bringing the inspirations of that
genius to the test of experiment. By the immortal experiments of Mr.
Joule, the mutual convertibility of mechanical work and heat was first
conclusively established. And “Joule’s equivalent,” as it is rightly
called, considering the amount of resolute labor and skill expended
in its determination, is almost identical with that derived from the
formula of Mayer.
§ 12. _Absence of Radiative Power of Air deduced from Velocity of Sound_
Consider now the ground we have trodden, the curious labyrinth of
reasoning and experiment through which we have passed. We started with
the observed and calculated velocities of sound in atmospheric air. We
found Laplace, by a special assumption, deducing from these velocities
the ratio of the specific heat of air at constant pressure to its
specific heat at constant volume. We found Mayer calculating from
this ratio the mechanical equivalent of heat; finally, we found Joule
determining the same equivalent by direct experiments on the friction
of solids and liquids. And what is the result? Mr. Joule’s experiments
prove the result of Mayer to be the true one; they therefore prove the
ratio determined by Laplace to be the true ratio; and, because they do
this, they prove at the same time the practical absence of radiative
power in atmospheric air. It seems a long step from the stirring of
water, or the rubbing together of iron plates in Joule’s experiments,
to the radiation of the atoms of our atmosphere; both questions are,
however, connected by the line of reasoning here followed out.
But the true physical philosopher never rests content with an
inference when an experiment to verify or contravene it is possible.
The foregoing argument is clinched by bringing the radiative power of
atmospheric air to a direct test. When this is done, experiment and
reasoning are found to agree; air being proved to be a body sensibly
devoid of radiative and absorptive power.[23]
But here the experimenter on the transmission of sound through gases
needs a word of warning. In Laplace’s day, and long subsequently, it
was thought that gases of all kinds possessed only an infinitesimal
power of radiation; but that this is not the case is now well
established. It would be rash to assume that, in the case of such
bodies as ammonia, aqueous vapor, sulphurous acid, and olefiant gas,
their enormous radiative powers do not interfere with the application
of the formula of Laplace. It behooves us to inquire whether the
ratio of the two specific heats deduced from the velocity of sound
in these bodies is the true ratio; and whether, if the true ratio
could be found by other methods, its square root, multiplied into the
calculated velocity, would give the observed velocity. From the moment
heat first appears in the condensation and cold in the rarefaction of
a sonorous wave in any of those gases, the radiative power comes into
play to abolish the difference of temperature. The condensed part of
the wave is on this account rendered more flaccid and the rarefied part
less flaccid than it would otherwise be, and with a sufficiently high
radiative power the velocity of sound, instead of coinciding with that
derived from the formula of Laplace, must approximate to that derived
from the more simple formula of Newton.
§ 13. _Velocity of Sound through Gases, Liquids, and Solids_
To complete our knowledge of the transmission of sound through gases,
a table is here added from the excellent researches of Dulong, who
employed in his experiments a method which shall be subsequently
explained:
VELOCITY OF SOUND IN GASES AT THE TEMPERATURE OF 0° C.
Velocity
Air 1,092 feet
Oxygen 1,040 ”
Hydrogen 4,164 ”
Carbonic acid 858 ”
Carbonic oxide 1,107 ”
Protoxide of nitrogen 859 ”
Olefiant gas 1,030 ”
According to theory, the velocities of sound in oxygen and hydrogen are
inversely proportional to the square roots of the densities of the two
gases. We here find this theoretic deduction verified by experiment.
Oxygen being sixteen times heavier than hydrogen, the velocity of
sound in the latter gas ought, according to the above law, to be four
times its velocity in the former; hence, the velocity in oxygen being
1,040, in hydrogen calculation would make it 4,160. Experiment, we see,
makes it 4,164.
The velocity of sound in liquids may be determined theoretically, as
Newton determined its velocity in air; for the density of a liquid is
easily determined, and its elasticity can be measured by subjecting it
to compression. In the case of water, the calculated and the observed
velocities agree so closely as to prove that the changes of temperature
produced by a sound-wave in water have no sensible influence upon the
velocity. In a series of memorable experiments in the Lake of Geneva,
MM. Colladon and Sturm determined the velocity of sound through water,
and made it 4,708 feet a second. By a mode of experiment which you will
subsequently be able to comprehend, the late M. Wertheim determined the
velocity through various liquids, and in the following table I have
collected his results:
TRANSMISSION OF SOUND THROUGH LIQUIDS
Name of Liquid Temperature Velocity
River-water (Seine) 15° C. 4,714 feet
” ” 30 5,013 ”
” ” 60 5,657 ”
Sea-water (artificial) 20 4,768 ”
Solution of common salt 18 5,132 ”
Solution of sulphate of soda 20 5,194 ”
Solution of carbonate of soda 22 5,230 ”
Solution of nitrate of soda 21 5,477 ”
Solution of chloride of calcium 23 6,493 ”
Common alcohol 20 4,218 ”
Absolute alcohol 23 3,804 ”
Spirits of turpentine 24 3,976 ”
Sulphuric ether 0 3,801 ”
We learn from this table that sound travels with different velocities
through different liquids; that a salt dissolved in water augments the
velocity, and that the salt which produces the greatest augmentation is
chloride of calcium. The experiments also teach us that in water, as in
air, the velocity augments with the temperature. At a temperature of
15° C., for example, the velocity in Seine water is 4,714 feet, at 30°
it is 5,013 feet, and at 60° 5,657 feet a second.
I have said that from the compressibility of a liquid, determined by
proper measurements, the velocity of sound through the liquid may
be deduced. Conversely, from the velocity of sound in a liquid, the
compressibility of the liquid may be deduced. Wertheim compared a
series of compressibilities deduced from his experiments on sound with
a similar series obtained directly by M. Grassi. The agreement of both,
exhibited in the following table, is a strong confirmation of the
accuracy of the method pursued by Wertheim:
Cubic compressibility
╭——————————————-——^————————————————╮
from Wertheim’s from the direct
velocity of sound experiments of
M. Grassi
Sea-water 0·0000467 0·0000436
Solution of common salt 0·0000349 0·0000321
” carbonate of soda 0·0000337 0·0000297
” nitrate of soda 0·0000301 0·0000295
Absolute alcohol 0·0000947 0·0000991
Sulphuric ether 0·0001002 0·0001110
The greater the resistance which a liquid offers to compression, the
more promptly and forcibly will it return to its original volume after
it has been compressed. The less the compressibility, therefore, the
greater is the elasticity, and consequently, other things being equal,
the greater the velocity of sound through the liquid.
We have now to examine the transmission of sound through solids. Here,
as a general rule, the elasticity, as compared with the density, is
greater than in liquids, and consequently the propagation of sound is
more rapid.
In the following table the velocity of sound through various metals, as
determined by Wertheim, is recorded:
VELOCITY OF SOUND THROUGH METALS
Name of Metal At 20° C. At 100° C. At 200° C.
Lead 4,030 3,951 ......
Gold 5,717 5,640 5,619
Silver 8,553 8,658 8,127
Copper 11,666 10,802 9,690
Platinum 8,815 8,437 8,079
Iron 16,822 17,386 15,483
Iron wire (ordinary) 16,130 16,728 ......
Cast steel 16,357 16,153 15,709
Steel wire (English) 15,470 17,201 16,394
Steel wire 16,023 16,443 ......
As a general rule, the velocity of sound through metals is diminished
by augmented temperature; iron is, however, a striking exception to
this rule, but it is only within certain limits an exception. While,
for example, a rise of temperature from 20° to 100° C. in the case of
copper causes the velocity to fall from 11,666 to 10,802, the same
rise produces in the case of iron an increase of velocity from 16,822
to 17,386. Between 100° and 200°, however, we see that iron falls from
the last figure to 15,483. In iron, therefore, up to a certain point,
the elasticity is augmented by heat; beyond that point it is lowered.
Silver is also an example of the same kind.
The difference of velocity in iron and in air may be illustrated by the
following instructive experiment: Choose one of the longest horizontal
bars employed for fencing in Hyde Park; and let an assistant strike the
bar at one end while the ear of the observer is held close to the bar
at a considerable distance from the point struck. Two sounds will reach
the ear in succession; the first being transmitted through the iron and
the second through the air. This effect was obtained by M. Biot, in his
experiments on the iron water-pipes of Paris.
The transmission of sound through a solid depends on the manner
in which the molecules of the solid are arranged. If the body be
homogeneous and without structure, sound is transmitted through it
equally well in all directions. But this is not the case when the body,
whether inorganic like a crystal or organic like a tree, possesses
a definite structure. This is also true of other things than sound.
Subjecting, for example, a sphere of wood to the action of a magnet,
it is not equally affected in all directions. It is repelled by the
pole of the magnet, but it is most strongly repelled when the force
acts along the fibre. Heat also is conducted with different facilities
in different directions through wood. It is most freely conducted
along the fibre, and it passes more freely across the ligneous layers
than along them. Wood, therefore, possesses _three unequal axes_ of
calorific conduction. These, established by myself, coincide with the
axes of elasticity discovered by Savart. MM. Wertheim and Chevandier
have determined the velocity of sound along these three axes and
obtained the following results:
VELOCITY OF SOUND IN WOOD
Name of Wood Along Fibre Across Rings Along Rings
Acacia 15,467 4,840 4,436
Fir 15,218 4,382 2,572
Beech 10,965 6,028 4,643
Oak 12,622 5,036 4,229
Pine 10,900 4,611 2,605
Elm 13,516 4,665 3,324
Sycamore 14,639 4,916 3,728
Ash 15,314 4,567 4,142
Alder 15,306 4,491 3,423
Aspen 16,677 5,297 2,987
Maple 13,472 5,047 3,401
Poplar 14,050 4,600 3,444
Separating a cube from the bark-wood of a good-sized tree, where the
rings for a short distance may be regarded as straight: then, if A R,
Fig. 14, be the section of the tree, the velocity of the sound in the
direction _m n_, through such a cube, is greater than in the direction
_a b_.
[Illustration: FIG. 14.]
The foregoing table strikingly illustrates the influence of molecular
structure. The great majority of crystals show differences of the same
kind. Such bodies, for the most part, have their molecules arranged
in different degrees of proximity in different directions, and where
this occurs there are sure to be differences in the transmission and
manifestation of heat, light, electricity, magnetism, and sound.
§ 14. _Hooke’s Anticipation of the Stethoscope_
I will conclude this lecture on the transmission of sound through
gases, liquids, and solids, by a quaint and beautiful extract from
the writings of that admirable thinker, Dr. Robert Hooke. It will be
noticed that the philosophy of the stethoscope is enunciated in the
following passage, and another could hardly be found which illustrates
so well that action of the scientific imagination which, in all great
investigators, is the precursor and associate of experiment:
“There may also be a possibility,” writes Hooke, “of discovering the
internal motions and actions of bodies by the sound they make. Who
knows but that, as in a watch, we may hear the beating of the balance,
and the running of the wheels, and the striking of the hammers, and the
grating of the teeth, and multitudes of other noises; who knows, I say,
but that it may be possible to discover the motions of the internal
parts of bodies, whether animal, vegetable, or mineral, by the sound
they make; that one may discover the works performed in the several
offices and shops of a man’s body, and thereby discover what instrument
or engine is out of order, what works are going on at several times,
and lie still at others, and the like; that in plants and vegetables
one might discover by the noise the pumps for raising the juice, the
valves for stopping it, and the rushing of it out of one passage into
another, and the like? I could proceed further, but methinks I can
hardly forbear to blush when I consider how the most part of men will
look upon this: but, yet again, I have this encouragement, not to think
all these things utterly impossible, though never so much derided
by the generality of men, and never so seemingly mad, foolish, and
fantastic, that as the thinking them impossible cannot much improve my
knowledge, so the believing them possible may, perhaps, be an occasion
of taking notice of such things as another would pass by without
regard as useless. And somewhat more of encouragement I have also from
experience, that I have been able to hear very plainly the beating of a
man’s heart, and it is common to hear the motion of wind to and fro in
the guts, and other small vessels; the stopping of the lungs is easily
discovered by the wheezing, the stopping of the head by the humming and
whistling noises, the slipping to and fro of the joints, in many cases,
by crackling, and the like, as to the working or motion of the parts
one among another; methinks I could receive encouragement from hearing
the hissing noise made by a corrosive menstruum in its operation, the
noise of fire in dissolving, of water in boiling, of the parts of a
bell after that its motion is grown quite invisible as to the eye, for
to me these motions and the other seem only to differ _secundum magis
minus_, and so to their becoming sensible they require either that
their motions be increased, or that the organ be made more nice and
powerful to sensate and distinguish them.”
NOTE ON THE DIFFRACTION OF SOUND
The recent explosion of a powder-laden barge in the Regent’s
Park produced effects similar to those mentioned in § 7.
The sound-wave bent round houses and broke the windows at
the back, the coalescence of different portions of the wave
at special points being marked by intensified local action.
Close to the place where the explosion occurred the unconsumed
gunpowder was in the wave, and, as a consequence, the
dismantled gatekeeper’s lodge was girdled all round by a black
belt of carbon.
SUMMARY OF CHAPTER I
The sound of an explosion is propagated as a wave or pulse through the
air.
This wave impinging upon the tympanic membrane causes it to shiver, its
tremors are transmitted to the auditory nerve, and along the auditory
nerve to the brain, where it announces itself as sound.
A sonorous wave consists of two parts, in one of which the air is
condensed, and in the other rarefied.
The motion of the sonorous wave must not be confounded with the motion
of the particles which at any moment form the wave. During the passage
of the wave every particle concerned in its transmission makes only a
small excursion to and fro.
The length of this excursion is called the _amplitude_ of the vibration.
Sound cannot pass through a vacuum.
A certain sharpness of shock, or rapidity of vibration, is needed for
the production of sonorous waves in air. It is still more necessary
in hydrogen, because the greater mobility of this light gas tends to
prevent the formation of condensations and rarefactions.
Sound is in all respects reflected like light; it is also refracted
like light; and it may, like light, be condensed by suitable lenses.
Sound is also diffracted, the sonorous wave bending round obstacles;
such obstacles, however, in part shade off the sound.
Echoes are produced by the reflected waves of sound.
In regard to sound and the medium through which it passes, four
distinct things are to be borne in mind—intensity, velocity,
elasticity, and density.
The intensity is proportional to the square of the amplitude as above
defined.
It is also proportional to the square of the maximum velocity of the
vibrating air-particles.
When sound issues from a small body in free air, the intensity
diminishes as the square of the distance from the body increases.
If the wave of sound be confined in a tube with a smooth interior
surface, it may be conveyed to great distances without sensible loss of
intensity.
The velocity of sound in air depends on the elasticity of the air in
relation to its density. The greater the elasticity the swifter is the
propagation; the greater the density the slower is the propagation.
The velocity is directly proportional to the square root of the
elasticity; it is inversely proportional to the square root of the
density.
Hence, if elasticity and density vary in the same proportion, the one
will neutralize the other as regards the velocity of sound.
That they do vary in the same proportion is proved by the law of Boyle
and Mariotte; hence the velocity of sound in air is independent of the
density of the air.
But that this law shall hold good, it is necessary that the dense air
and the rare air should have the same temperature.
The intensity of a sound depends upon the density of the air in which
it is generated, but not on that of the air in which it is heard.
The velocity of sound in air of the temperature 0° C. is 1,090 feet a
second; it augments nearly 2 feet for every degree Centigrade added to
its temperature.
Hence, given the velocity of sound in air, the temperature of the air
may be readily calculated.
The distance of a fired cannon or of a discharge of lightning may be
determined by observing the interval which elapses between the flash
and the sound.
From the foregoing, it is easy to see that if a row of soldiers form a
circle, and discharge their pieces all at the same time, the sound will
be heard as a single discharge by a person occupying the centre of the
circle.
But if the men form a straight row, and if the observer stand at one
end of the row, the simultaneous discharge of the men’s pieces will be
prolonged to a kind of roar.
A discharge of lightning along a lengthy cloud may in this way produce
the prolonged roll of thunder. The roll of thunder, however, must in
part at least be due to echoes from the clouds.
The pupil will find no difficulty in referring many common occurrences
to the fact that sound requires a sensible time to pass through any
considerable length of air. For example, the fall of the axe of a
distant wood-cutter is not simultaneous with the sound of the stroke.
A company of soldiers marching to music along a road cannot march
in time, for the notes do not reach those in front and those behind
simultaneously.
In the condensed portion of a sonorous wave the air is above, in the
rarefied portion of the wave it is below, its average temperature.
This change of temperature, produced by the passage of the sound-wave
itself, virtually augments the elasticity of the air, and makes the
velocity of sound about one-sixth greater than it would be if there
were no change of temperature.
The velocity found by Newton, who did not take this change of
temperature into account, was 916 feet a second.
Laplace proved that by multiplying Newton’s velocity by the square root
of the ratio of the specific heat of air at constant pressure to its
specific heat at constant volume, the actual or observed velocity is
obtained.
Conversely, from a comparison of the calculated and observed
velocities, the ratio of the two specific heats may be inferred.
The mechanical equivalent of heat may be deduced from this ratio; it is
found to be the same as that established by direct experiment.
This coincidence leads to the conclusion that atmospheric air is devoid
of any sensible power to radiate heat. Direct experiments on the
radiative power of air establish the same result.
The velocity of sound in water is more than four times its velocity in
air.
The velocity of sound in iron is seventeen times its velocity in air.
The velocity of sound along the fibre of pine-wood is ten times its
velocity in air.
The cause of this great superiority is that the elasticities of the
liquid, the metal, and the wood, as compared with their respective
densities, are vastly greater than the elasticity of air in relation to
its density.
The velocity of sound is dependent to some extent upon molecular
structure. In wood, for example, it is conveyed with different degrees
of rapidity in different directions.