High Frequency Sound Radiation from a Diaphragm

Abstract

Calculation of the intensity of the high frequency sound radiation from a circular oscillator.—By a hydrodynamical-acoustical method a calculation is made of the intensity of the high frequency sound radiation from a circular piston-like oscillator at a distance from the oscillator greater than $2a$, where $a$ is the radius. It is shown that there is no parallel "beam" of sound of cross-sectional area equal to the area of the oscillator, but that nevertheless most of the sound energy is contained in a cone of solid angle $\pi {\left(\frac{0.45\lambda }{a}\right)}^2$ ster-radians where $\lambda$ is the wave-length of the radiation. Solution of the problem for points at great relative distance from the source then yields a result analogous to that obtained for the Fraunhofer diffraction of light through a circular aperture. The corresponding formula is $\pi {\left(\frac{0.61\lambda }{a}\right)}^2$. Comparison is made between the two methods and they are shown to be essentially the same, the difference in the formulae being due to difference in interpretation solely.