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ACOUSTICS
1.Acoustics (from ἀκούω, to hear) is that branch of Natural Philosophy which treats of the nature of sound, and the laws of its production and propagation, in so far as these depend on physical principles. The description of the mechanism of the organ of voice and of the ear, and the difficult questions connected with the processes by which, when sound reaches the drum of the ear, it is transmitted to the brain, must be dealt with in separate articles of this work. It is to the physical part of the science of acoustics that the present article is restricted.
PART I.
General notions as to Vibrations, Waves, &c.
2.We may easily satisfy ourselves that, in every instance in which the sensation of sound is excited, the body, whence the sound proceeds, must have been thrown, by a blow or other means, into a state of agitation or tremor, implying the existence of a vibratory motion, or motion to and fro, of the particles of which it consists.
Thus, if a common glass-jar be struck so as to yield an audible sound, the existence of a motion of this kind may be felt by the finger lightly applied to the edge of the glass; and, on increasing the pressure so as to destroy this motion, the sound forthwith ceases. Small pieces of cork put in the jar will be found to dance about during the continuance of the sound; water or spirits of wine poured into the glass will, under the same circumstances, exhibit a ruffled surface. The experiment is usually performed, in a more striking manner, with a bell-jar and a number of small light wooden balls suspended by silk strings to a fixed frame above the jar, so as to be just in contact with the widest part of the glass. On drawing a violin bow across the edge, the pendulums are thrown off to a considerable distance, and falling back are again repelled, &c.
It is also in many cases possible to follow with the eye the motions of the particles of the sounding body, as, for instance, in the case of a violin string or any string fixed at both ends, when the string will appear, by a law of optics, to occupy at once all the positions which it successively assumes during its vibratory motion.
3.It is, moreover, essential, in order that the ear may be affected by a sounding body, that there be interposed between it and the ear one or more intermediate bodies (media), themselves capable of molecular vibration, which shall receive such motion from the source of sound, and transmit it to the external parts of the ear, and especially to the membrana tympani or drum of the ear. This statement is confirmed by the well-known effect of stopping the ear with soft cotton, or other substance possessing little elasticity.
The air around us forms the most important medium of communication of sound to our organs of hearing; in fact, were air devoid of this property, we should practically be without the sense of hearing. In illustration of the part thus assigned to the atmosphere in acoustics, an apparatus has been constructed, consisting of a glass receiver, in which is a bell and a hammer connected with clock-work, by which it can be made to strike the bell when required. The receiver is closed air-tight by a metal plate, through which passes, also air-tight, into the interior, a brass rod. By properly moving this rod with the hand, a detent is released, which checks the motion of the wheel-work, and the hammer strikes the bell continuously, till the detent is pushed into its original position. As long as the air in the receiver is of the usual atmospheric density, the sound is perfectly audible. But on rarefying the air by means of an air-pump (the clock-work apparatus having been separated from the plate of the pump by means of a pad ding of soft cotton), the sound grows gradually fainter, and at last becomes inaudible when the rarefaction of the air has reached a very low point. If, however, at this stage of the experiment, the metal rod be brought into contact with the bell, the sound will again be heard clearly, because now there is the necessary communication with the ear. On readmitting the air, the sound recovers its original intensity. This experiment was first performed by Hawksbee in 1705.
4.Inasmuch, then, as sound necessarily implies the Laws of existence in the sounding body, in the air, &c., and (we may add) in the ear itself, of vibratory motion of the particles of the various media concerned in the phenomenon, a general reference to the laws of such motion is essential to a right understanding of the principles of acoustics.
The most familiar instance of this kind of motion is afforded by the pendulum, a small heavy ball, for instance, attached to a fine string, which is fixed at its other end. There is but one position in which the ball will remain at rest, viz., when the string is vertical, there being then equilibrium between the two forces acting on the body, the tension of the string and the earth's attractive force or gravity. Thus, in the adjoining fig., if is the point of suspension, and the vertical through that point of length , equal to the string, is the equilibrium position of the particle.
Fig. 1.
Let now the ball be removed from to , the string being kept tight, so that describes the arc of a circle of radius equal to , and let the ball be there dropped. The tension of the string not being now directly opposite in direction to gravity (), motion will ensue, and the body will retrace the arc . In doing so, it will continually increase its velocity until it reaches the point , where its velocity will be a maximum, and will consequently pass to the other side of towards . But now gravity tends to draw it back towards , and hence the motion becomes a retarded one; the velocity continually diminishes, and is ultimately destroyed at some point , which would be at a distance from equal to that of , but for the existence of friction, resistance of the air, &c., which make that distance less. From it will next move down with accelerated motion towards , where it will have its greatest velocity in the direction from left to right, and whence it will pass onwards towards , and so on. Thus the body will vibrate to and fro on either side of , its amplitude of vibration or distance between its extreme positions gradually diminishing in consequence of the resistances before mentioned, and at last being sensibly reduced to nothing, the body then resuming its equilibrium-position .
If the amplitude of vibration is restricted within inconsiderable limits, it is easy to prove that the motion takes place just as if the string were removed, the ball deprived altogether of weight and urged by a force directed to the point , and proportional to the distance from that point. For then, if be any position of the ball, the chord may be regarded as coincident with the tangent to the
