In designing "sound generators" it is important to observe that the sound energy radiated bears a definite relation to the total energy available at the source. The conditions governing efficien cy in this connection are similar to the analogous case of an electrical generator supplying power to an external circuit.
"Local Flow."—When the vibrations of a solid body immersed in a fluid medium are very slow, the fluid behaves as if it were incompressible and simply flows locally from one surface of the "double source" to the other surface in opposite phase. In that case no sensible vibration is transmitted through the medium. As the vibrations increase in frequency the local flow is reduced, whilst true alternating pressure-waves, i.e., sound-waves, are set up in the medium. Again, at constant frequency, the higher the velocity of sound in the medium, the more nearly does the medium approach incompressibility, consequently the local flow is greater and less energy is radiated as sound.
On all grounds it is clearly preferable to use the simple source rather than the double source type of sound generator, for the local flow is reduced and there is no neutralising effect due to "out of phase vibrations" from a neighbouring surface. The increase of sound radiated from a tuning fork when "local flow" is reduced, may easily be demonstrated (see fig. 9). A piece of cardboard is held with one edge parallel and close to a prong of the vibrating fork. In positions A and B no effect is produced, whereas at C the sound is considerably increased in intensity.
The Principle of Superposition.—Huyghens first drew atten tion to the fact that the passage of one beam of light through an aperture is in no way affected by the passage of another beam through the same aperture. It is a commonplace observation that any number of sound-waves may cross the same air space at the same time without the slightest evidence of confusion due to overlapping. This independence of the separate waves is explained by the principle of superposition, according to which the resultant effect of a number of displacements may be ob tained by vector addition. The validity of this important prin ciple is dependent on the as sumption that the elastic proper ties of the medium are such that the stresses are linear functions of the strains—a condition which is fulfilled in the case of small-amplitude sound-waves.
Huyghens' Secondary Waves.—Another important principle due to Huyghens is the following:—The wave-front of a dis turbance may at any instant be obtained as the envelope of the secondary waves proceeding from all points of the wave-front at some preceding instant. Thus the disturbance diverging from a point source may at any time t be regarded as represented by a thin spherical shell of radius ct, each point of which now serves as the origin of further spherical disturbances, the envelope of which becomes the new wave-front.