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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 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 ex
periment. 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 in
tensity, 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. 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 tuningfork 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.