Sound—Propagation of Sound illustrated by a Field of Standing
Corn—Nature of Waves—Propagation of Sound through the
Atmosphere—Intensity—Noises—A Musical Sound—Quality—Pitch—Extent of
Human Hearing—Velocity of Sound in Air, Water, and Solids—Causes of
the Obstruction of Sound—Law of its Intensity—Reflection of
Sound—Echoes—Thunder—Refraction of Sound—Interference of Sounds.
ONE of the most important uses of the atmosphere is the conveyance of
sound. Without the air, deathlike silence would prevail through nature,
for in common with all substances it has a tendency to impart vibrations
to bodies in contact with it. Therefore undulations received by the air,
whether it be from a sudden impulse, such as an explosion or the
vibrations of a musical chord, are propagated in every direction, and
produce the sensation of sound upon the auditory nerves. A bell rung
under the exhausted receiver of an air-pump is inaudible, which shows
that the atmosphere is really the medium of sound. In the small
undulations of deep water in a calm, the vibrations of the liquid
particles are made in the vertical plane, that is, up and down, or at
right angles to the direction of the transmission of the waves. But the
vibrations of the particles of air which produce sound differ from
these, being performed in the same direction in which the waves of sound
travel. The propagation of sound has been illustrated by a field of corn
agitated by the wind. However irregular the motion of the corn may seem
on a superficial view, it will be found, if the velocity of the wind be
constant, that the waves are all precisely similar and equal, and that
all are separated by equal intervals and move in equal times.
A sudden blast depresses each ear equally and successively in the
direction of the wind, but, in consequence of the elasticity of the
stalks and the force of the impulse, each ear not only rises again as
soon as the pressure is removed, but bends back nearly as much in the
contrary direction, and then continues to oscillate backwards and
forwards in equal times, like a pendulum, to a less and less extent,
till the resistance of the air puts a stop to the motion. These
vibrations are the same for every individual ear of corn. Yet, as their
oscillations do not all commence at the same time, but successively, the
ears will have a variety of positions at any one instant. Some of the
advancing ears will meet others in their returning vibrations, and, as
the times of oscillation are equal for all, they will be crowded
together at regular intervals. Between these there will occur equal
spaces where the ears will be few, in consequence of being bent in
opposite directions; and at other equal intervals they will be in their
natural upright positions. So that over the whole field there will be a
regular series of condensations and rarefactions among the ears of corn,
separated by equal intervals, where they will be in their natural state
of density. In consequence of these changes the field will be marked by
an alternation of bright and dark bands. Thus the successive waves which
fly over the corn with the speed of the wind are totally distinct from,
and entirely independent of the extent of the oscillations of each
individual ear, though both take place in the same direction. The length
of a wave is equal to the space between two ears precisely in the same
state of motion, or which are moving similarly, and the time of the
vibration of each ear is equal to that which elapses between the arrival
of two successive waves at the same point. The only difference between
the undulations of a corn-field and those of the air which produce sound
is, that each ear of corn is set in motion by an external cause, and is
uninfluenced by the motion of the rest; whereas in air, which is a
compressible and elastic fluid, when one particle begins to oscillate,
it communicates its vibrations to the surrounding particles, which
transmit them to those adjacent, and so on continually. Hence from the
successive vibrations of the particles of air the same regular
condensations and rarefactions take place as in the field of corn,
producing waves throughout the whole mass of air, though each molecule
like each individual ear of corn never moves far from its state of rest.
The small waves of a liquid, and the undulations of the air, like waves
in the corn, are evidently not real masses moving in the direction in
which they are advancing, but merely outlines, motions, or forms passing
along, and comprehending all the particles of an undulating fluid which
are at once in a vibratory state. It is thus that an impulse given to
any one point of the atmosphere is successively propagated in all
directions, in a wave diverging as from the centre of a sphere to
greater and greater distances, but with decreasing intensity, in
consequence of the increasing number of particles of inert matter which
the force has to move; like the waves formed in still water by a falling
stone, which are propagated circularly all around the centre of
disturbance (N. 160).
The intensity of sound depends upon the violence and extent of the
initial vibrations of air; but, whatever they may be, each undulation
when once formed can only be transmitted straight forwards, and never
returns back again unless when reflected by an opposing obstacle. The
vibrations of the aërial molecules are always extremely small, whereas
the waves of sound vary from a few inches to several feet. The various
musical instruments, the human voice and that of animals, the singing of
birds, the hum of insects, the roar of the cataract, the whistling of
the wind, and the other nameless peculiarities of sound, show at once an
infinite variety in the modes of aërial vibration, and the astonishing
acuteness and delicacy of the ear, thus capable of appreciating the
minutest differences in the laws of molecular oscillation.
All mere noises are occasioned by irregular impulses communicated to the
ear; and, if they be short, sudden, and repeated beyond a certain degree
of quickness, the ear loses the intervals of silence, and the sound
appears continuous. Still such sounds will be mere noise: in order to
produce a musical sound, the impulses, and consequently the undulations
of the air, must be all exactly similar in duration and intensity, and
must recur after exactly equal intervals of time. If a blow be given to
the nearest of a series of broad, flat, and equidistant palisades, set
edgewise in a line direct from the ear, each palisade will repeat or
echo the sound; and these echoes, returning to the ear at successive
equal intervals of time, will produce a musical note. The quality of a
musical note depends upon the abruptness, and its intensity upon the
violence and extent of the original impulse. In the theory of harmony
the only property of sound taken into consideration is the pitch, which
varies with the rapidity of the vibrations. The grave or low tones are
produced by very slow vibrations, which increase in frequency as the
note becomes more acute. The lowest man’s voice makes 396 vibrations in
a second, whilst the highest woman’s voice makes 2112. Very deep tones
are not heard by all alike, and Dr. Wollaston, who made a variety of
experiments on the sense of hearing, found that many people, though not
at all deaf, are quite insensible to the cry of the bat or the cricket,
while to others it is painfully shrill. From his experiments he
concluded that human hearing is limited to about nine octaves, extending
from the lowest note of the organ to the highest known cry of insects;
and he observes with his usual originality that, “as there is nothing in
the nature of the atmosphere to prevent the existence of vibrations
incomparably more frequent than any of which we are conscious, we may
imagine that animals like the Grylli, whose powers appear to commence
nearly where ours terminate, may have the faculty of hearing still
sharper sounds which we do not know to exist, and that there may be
other insects hearing nothing in common with us, but endowed with a
power of exciting, and a sense which perceives vibrations, of the same
nature indeed as those which constitute our ordinary sounds, but so
remote that the animals which perceive them may be said to possess
another sense, agreeing with our own solely in the medium by which it is
excited.”
M. Savart, so well known for the number and beauty of his researches in
acoustics, has proved that a high note of a given intensity, being heard
by some ears and not by others, must not be attributed to its pitch, but
to its feebleness. His experiments, and those more recently made by
Professor Wheatstone, show that, if the pulses could be rendered
sufficiently powerful, it would be difficult to fix a limit to human
hearing at either end of the scale. M. Savart had a wheel made about
nine inches in diameter with 360 teeth set at equal distances round its
rim, so that while in motion each tooth successively hit on a piece of
card. The tone increased in pitch with the rapidity of the rotation, and
was very pure when the number of strokes did not exceed three or four
thousand in a second, but beyond that it became feeble and indistinct.
With a wheel of a larger size a much higher tone could be obtained,
because, the teeth being wider apart, the blows were more intense and
more separated from one another. With 720 teeth on a wheel thirty-two
inches in diameter, the sound produced by 12,000 strokes in a second was
audible, which corresponds to 24,000 vibrations of a musical chord. So
that the human ear can appreciate a sound which only lasts the 24,000th
part of a second. This note was distinctly heard by M. Savart and by
several people who were present, which convinced him that with another
apparatus still more acute sounds might be rendered audible.
For the deep tones M. Savart employed a bar of iron, two feet eight
inches long, about two inches broad, and half an inch in thickness,
which revolved about its centre as if its arms were the spokes of a
wheel. When such a machine rotates, it impresses a motion on the air
similar to its own, and, when a thin board or card is brought close to
its extremities, the current of air is momentarily interrupted at the
instant each arm of the bar passes before the card; it is compressed
above the card and dilated below; but the instant the spoke has passed a
rush of air to restore equilibrium makes a kind of explosion, and, when
these succeed each other rapidly, a musical note is produced of a pitch
proportional to the velocity of the revolution. When M. Savart turned
this bar slowly, a succession of single beats was heard; as the velocity
became greater, the sound was only a rattle; but, as soon as it was
sufficient to give eight beats in a second, a very deep musical note was
distinctly audible corresponding to sixteen single vibrations in a
second, which is the lowest that has hitherto been produced. When the
velocity of the bar was much increased, the intensity of the sound was
hardly bearable. The spokes of a revolving wheel produce the sensation
of sound, on the very same principle that a burning stick whirled round
gives the impression of a luminous circle. The vibrations excited in the
organ of hearing by one beat have not ceased before another impulse is
given. Indeed it is indispensable that the impressions made upon the
auditory nerves should encroach upon each other in order to produce a
full and continued note. On the whole, M. Savart has come to the
conclusion, that the most acute sounds would be heard with as much ease
as those of a lower pitch, if the duration of the sensation produced by
each pulse could be diminished proportionally to the augmentation of the
number of pulses in a given time: and on the contrary, if the duration
of the sensation produced by each pulse could be increased in proportion
to their number in a given time, that the deepest tones would be as
audible as any of the others.
The velocity of sound is uniform and independent of the nature, extent,
and intensity of the primitive disturbance. Consequently sounds of every
quality and pitch travel with equal speed. The smallest difference in
their velocity is incompatible either with harmony or melody, for notes
of different pitches and intensities, sounded together at a little
distance, would arrive at the ear in different times. A rapid succession
of notes would in this case produce confusion and discord. But, as the
rapidity with which sound is transmitted depends upon the elasticity of
the medium through which it has to pass, whatever tends to increase the
elasticity of the air must also accelerate the motion of sound. On that
account its velocity is greater in warm than in cold weather, supposing
the pressure of the atmosphere constant. In dry air, at the freezing
temperature, sound travels at the rate of 1090 feet in a second, and for
any higher temperature one foot must be added for every degree of the
thermometer above 32°: hence at 62° of Fahrenheit its speed in a second
is 1120 feet, or 765 miles an hour, which is about three-fourths of the
diurnal velocity of the earth’s equator. Since all the phenomena of the
transmission of sound are simple consequences of the physical properties
of the air, they have been predicted and computed rigorously by the laws
of mechanics. It was found, however, that the velocity of sound,
determined by observation, exceeded what it ought to have been
theoretically by 173 feet, or about one-sixth of the whole amount. La
Place suggested that this discrepancy might arise from the increased
elasticity of the air in consequence of a development of latent or
absorbed heat (N. 178) during the undulations of sound, and calculation
confirmed the accuracy of his views. The aërial molecules being suddenly
compressed give out their absorbed heat; and, as air is too bad a
conductor to carry it rapidly off, it occasions a momentary and local
rise of temperature, which, increasing the elasticity of the air without
at the same time increasing its inertia, causes the movement to be
propagated more rapidly. Analysis gives the true velocity of sound in
terms of the elevation of temperature that a mass of air is capable of
communicating to itself, by the disengagement of its own absorbed heat
when suddenly compressed in a given ratio. This change of temperature
however could not be obtained _directly_ by any experiments which had
been made at that epoch; but by inverting the problem, and assuming the
velocity of sound as given by experiment, it was computed that the
temperature of a mass of air is raised nine-tenths of a degree when the
compression is equal to 1/116 of its volume.
Probably all liquids are elastic, though considerable force is required
to compress them. Water suffers a condensation of nearly 0·0000496 for
every atmosphere of pressure, and is consequently capable of conveying
sound even more rapidly than air, the velocity in the former being 4708
feet in a second. A person under water hears sounds made in air feebly,
but those produced in water very distinctly. According to the
experiments of M. Colladon, the sound of a bell was conveyed under water
through the Lake of Geneva to the distance of about nine miles. He also
perceived that the progress of sound through water is greatly impeded by
the interposition of any object, such as a projecting wall; consequently
sound under water resembles light in having a distinct shadow. It has
much less in air, being transmitted all round buildings or other
obstacles, so as to be heard in every direction, though often with a
considerable diminution of intensity, as when a carriage turns the
corner of a street.
The velocity of sound in passing through solids is in proportion to
their hardness, and is much greater than in air or water. A sound which
takes some time in travelling through the air passes almost
instantaneously along a wire six hundred feet long; consequently it is
heard twice—first as communicated by the wire, and afterwards through
the medium of the air. The facility with which the vibrations of sound
are transmitted along the grain of a log of wood is well known. Indeed
they pass through iron, glass, and some kinds of wood, at the rate of
18,530 feet in a second. The velocity of sound is obstructed by a
variety of circumstances, such as falling snow, fog, rain, or any other
cause which disturbs the homogeneity of the medium through which it has
to pass. M. de Humboldt says that it is on account of the greater
homogeneity of the atmosphere during the night that sounds are then
better heard than during the day, when its density is perpetually
changing from partial variations of temperature. His attention was
called to this subject on the plain surrounding the Mission of the
Apures by the rushing noise of the great cataracts of the Orinoco, which
seemed to be three times as loud by night as by day. This he illustrated
by experiment. A tall glass half full of champagne cannot be made to
ring as long as the effervescence lasts. In order to produce a musical
note, the glass together with the liquid it contains must vibrate in
unison as a system, which it cannot do in consequence of the fixed air
rising through the wine and disturbing its homogeneity, because, the
vibrations of the gas being much slower than those of the liquid, the
velocity of the sound is perpetually interrupted. For the same reason
the transmission of sound as well as light is impeded in passing through
an atmosphere of variable density. Sir John Herschel, in his admirable
Treatise on Sound, thus explains the phenomenon:—“It is obvious,” he
says, “that sound as well as light must be obstructed, stifled, and
dissipated from its original direction by the mixture of air of
different temperatures, and consequently elasticities; and thus the same
cause which produces that extreme transparency of the air at night,
which astronomers alone fully appreciate, renders it also more
favourable to sound. There is no doubt, however, that the universal and
dead silence generally prevalent at night renders our auditory nerves
sensible to impressions which would otherwise escape notice. The analogy
between sound and light is perfect in this as in so many other respects.
In the general light of day the stars disappear. In the continual hum of
voices, which is always going on by day, and which reach us from all
quarters, and never leave the ear time to attain complete tranquillity,
those feeble sounds which catch our attention at night make no
impression. The ear, like the eye, requires long and perfect repose to
attain its utmost sensibility.”
Many instances may be brought in proof of the strength and clearness
with which sound passes over the surface of water or ice. Lieutenant
Forster was able to carry on a conversation across Port Bowen Harbour,
when frozen, a distance of a mile and a half.
The intensity of sound depends upon the extent of the excursions of the
fluid molecules, on the energy of the transient condensations and
dilatations, and on the greater or less number of particles which
experience these effects. We estimate that intensity by the impetus of
these fluid molecules on our organs, which is consequently as the square
of the velocity, and not by their inertia, which is as the simple
velocity. Were the latter the case, there would be no sound, because the
inertia of the receding waves of air would destroy the equal and
opposite inertia of those advancing; whence it may be concluded that the
intensity of sound diminishes inversely as the square of the distance
from its origin. In a tube, however, the force of sound does not decay
as in open air, unless perhaps by friction against the sides. M. Biot
found, from a number of highly-interesting experiments made on the pipes
of the aqueducts in Paris, that a continued conversation could be
carried on in the lowest possible whisper through a cylindrical tube
about 3120 feet long, the time of transmission through that space being
2·79 seconds. In most cases sound diverges in all directions so as to
occupy at any one time a spherical surface; but Dr. Young has shown that
there are exceptions, as, for example, when a flat surface vibrates only
in one direction. The sound is then most intense when the ear is at
right angles to the surface, whereas it is scarcely audible in a
direction precisely perpendicular to its edge. In this case it is
impossible that the whole of the surrounding air can be affected in the
same manner, since the particles behind the sounding surface must be
moving towards it whenever the particles before it are retreating. Hence
in one half of the surrounding sphere of air its motions are retrograde,
while in the other half they are direct; consequently, at the edges
where these two portions meet, the motions of the air will neither be
retrograde nor direct, and therefore it must be at rest.
It appears, from theory as well as daily experience, that sound is
capable of reflection from surfaces (N. 179) according to the same laws
as light. Indeed any one who has observed the reflection of the waves
from a wall on the side of a river, after the passage of a steam-boat,
will have a perfect idea of the reflection of sound and of light. As
every substance in nature is more or less elastic, it may be agitated
according to its own law by the impulse of a mass of undulating air; and
reciprocally the surface by its reaction will communicate its
undulations back again into the air. Such reflections produce echoes;
and as a series of them may take place between two or more obstacles,
each will cause an echo of the original sound, growing fainter and
fainter till it dies away; because sound, like light, is weakened by
reflection. Should the reflecting surface be concave towards a person,
the sound will converge towards him with increased intensity, which will
be greater still if the surface be spherical and concentric with him.
Undulations of sound diverging from one focus of an elliptical shell
(N. 180) converge in the other after reflection. Consequently a sound
from the one will be heard in the other as if it were close to the ear.
The rolling noise of thunder has been attributed to reverberation
between different clouds, which may possibly be the case to a certain
extent. Sir John Herschel is of opinion that an intensely prolonged peal
is probably owing to a combination of sounds, because, the velocity of
electricity being incomparably greater than that of sound, the thunder
may be regarded as originating in every point of a flash of lightning at
the same instant. The sound from the nearest point will arrive first;
and if the flash run in a direct line from a person, the noise will come
later and later from the remote points of its path in a continued roar.
Should the direction of the flash be inclined, the succession of sounds
will be more rapid and intense: and if the lightning describe a circular
curve round a person, the sound will arrive from every point at the same
instant with a stunning crash. In like manner the subterranean noises
heard during earthquakes like distant thunder may arise from the
consecutive arrival at the ear of undulations propagated at the same
instant from nearer and more remote points; or if they originate in the
same point, the sound may come by different routes through strata of
different densities.
Sounds under water are heard very distinctly in the air immediately
above; but the intensity decays with great rapidity as the observer goes
farther off, and is altogether inaudible at the distance of two or three
hundred yards. So that waves of sound, like those of light, in passing
from a dense to a rare medium, are not only refracted, but suffer total
reflection at very oblique incidences (N. 189).
The laws of interference extend also to sound. It is clear that two
equal and similar musical strings will be in unison if they communicate
the same number of vibrations to the air in the same time. But if two
such strings be so nearly in unison that one performs a hundred
vibrations in a second, and the other a hundred and one in the same
period—during the first few vibrations the two resulting sounds will
combine to form one of double the intensity of either, because the
aërial waves will sensibly coincide in time and place; but one will
gradually gain on the other till at the fiftieth vibration it will be
half an oscillation in advance. Then the waves of air which produce the
sound being sensibly equal, but the receding part of the one coinciding
with the advancing part of the other, they will destroy one another, and
occasion an instant of silence. The sound will be renewed immediately
after, and will gradually increase till the hundredth vibration, when
the two waves will combine to produce a sound double the intensity of
either. These intervals of silence and greatest intensity, called beats,
will recur every second; but if the notes differ much from one another,
the alternations will resemble a rattle; and if the strings be in
perfect unison, there will be no beats, since there will be no
interference. Thus by interference is meant the co-existence of two
undulations in which the lengths of the waves are the same. And as the
magnitude of an undulation may be diminished by the addition of another
transmitted in the same direction, it follows that one undulation may be
absolutely destroyed by another when waves of the same length are
transmitted in the same direction, provided that the maxima of the
undulations are equal, and that one follows the other by half the length
of a wave. A tuning-fork affords a good example of interference. When
that instrument vibrates, its two branches alternately recede from and
approach one another; each communicates its vibrations to the air, and a
musical note is the consequence. If the fork be held upright about a
foot from the ear, and turned round its axis while vibrating, at every
quarter revolution the sound will scarcely be heard, while at the
intermediate points it will be strong and clear. This phenomenon arises
from the interference of the undulations of air coming from the two
branches of the fork. When the two branches coincide, or when they are
at equal distances from the ear, the waves of air combine to reinforce
each other; but at the quadrants, where the two branches are at unequal
distances from the ear, the lengths of the waves differ by half an
undulation, and consequently destroy one another.