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vibrations of the aërial molecules are always extremely small, whereas the waves of sound vary from a few inches to several feet. The various kinds of 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, at once show an infinite variety in the modes of aërial vibrations, 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, because, like the eye, it retains the perception of excitement for a moment after the impulse has ceased. Or, in other words, the auditory nerves continue their vibrations for an extremely short period after the impulse, before they return to a state of repose. 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. The quality of a musical note depends upon the abrupt
ness, and its intensity upon the violence and extent of the original impulse. But the whole theory of harmonics is founded upon 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 progressively, as the note becomes more acute. When the vibrations of a musical chord, for example, are less than sixteen in a second, it will not communicate a continued sound to the ear; the vibrations or pulses increase in number with the acuteness of the note till, at last, all sense of pitch is lost. The whole extent of human hearing, from the lowest note of the organ to the highest known cry of insects, as of the cricket, includes about nine octaves. All ears, however, are by no means gifted with so great a range of hearing; 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. According to recent experiments by M. Savart, the human ear is capable of hearing sounds arising from about 24000 vibrations in a second, and is consequently able to appreciate a sound which only lasts the twenty-four thousandth part of a second. All people do not hear the deep sounds alike; that faculty seems to depend upon the frequency of the vibrations, and not on the intensity or loudness.
But, although there are limits to the vibrations of our auditory nerves, Dr. Wollaston, who has investigated this curious subject with his usual originality, observes, 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 who perceive them may be said to possess another sense agreeing with our own solely in the medium by which it is excited."
The velocity of sound is uniform, and is 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; and a rapid succession of notes
would 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 1089 feet in a second, and at 62° of Fahrenheit, its speed is 1090 feet in the same time, or 765 miles an hour, which is about three-fourths of the diurnal velocity of the earth's equator. Since all the phenomena 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 heat during the undulations of sound, and the result of calculation fully confirmed the accuracy of his views. The aërial molecules being suddenly compressed give out their latent 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 consecutive expansion of the air, causes a still greater development of heat, and as it exceeds that which is absorbed in the next rarefaction, the air becomes yet warmer, which favours the transmission of sound. 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 latent heat, when it is suddenly compressed in a given ratio. This change of temperature, however, cannot be obtained directly by experiment; 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 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