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The formula obtained by Maa for the frequency distribution of the normal modes for a rectangular enclosure has been verified by a more direct computation and extended to apply to a cylinder, a sphere, and to a number of derived shapes. In all cases it is found that the number of normal modes with frequencies less than ν is given by 4πVν3/3c3+πAν2/4c2+⋯, where V is the volume and A the surface area of the enclosure. The application of this result is illustrated by a calculation of resonance response and rate of decay of sound in a cylinder.
Glenn M. Roe (Tue,) studied this question.