The Theory of Sound

Abstract

THE second part of Lord Rayleigh's highly instructive work on acoustics contains the mechanics of oscillatory motions in liquids and gases. Atmospheric air is that medium by which by far the greater number of sound-waves are conveyed to our ear, since it is only exceptional that this happens through solid bodies which are in contact with our teeth or with the bones of the skull. But it is just for this reason that all circumstances are of considerable importance, which influence the transmission of sound-waves in the air, i.e., change either their velocity, their direction, or their intensity. This part of the theory has been worked out very minutely and completely by the author. We find here the compilation and demonstration of a large number of facts which, in other works on acoustics, are hardly mentioned. The author, after having first developed (in Chap. XI.) the general laws of the motion of liquids as expressed in hydrodynamical equations, and then explained the difference between rotational and irrotational motion of fluids, passes on to the simplification of the equations, which is determined by the circumstance that with sound, as a rule, we have to do with oscillations of extremely small amplitude. First, the motion of plane waves is investigated, and it is shown that with waves which move only in one direction half their equivalent of work consists in the vis viva of motion, and the other half in the potential energy of the compression and dilatation of the medium. Then follows the explanation of the influence which the change of temperature, taking place with compression or dilatation of gases, exercises upon the velocity of transmission of sound. It is shown, in the manner first employed by Prof. Stokes, that if a perceptible quantity of heat could be exchanged between the compressed and dilated layers of the waves during the lapse of one oscillation, the intensity of the sound-waves would very quickly decrease in their transmision and they would die away.

The Theory of Sound.

By J. W. Strutt Baron Rayleigh. Vol. II. (London: Macmillan and Co., 1878.)¹