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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 320: 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 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