Reverberation in spherical rooms with nonuniform absorption.

The reverberation time of a room can be found from an eigenvalue of an integral equation, derived by Kuttruff and Joyce. Because the integral equation is difficult, exact reverberation times are known only for very simply shaped rooms. Here the room is a diffusely reflecting sphere, but with absorption coefficient alpha (P) that varies with position P on the sphere's surface. This room, admittedly an oversimplified model of real rooms, allows two interesting comparisons. One is between the room's true reverberation time and that predicted by the usual approximate formulas of Sabine, Eyring, et al. Another comparison shows the effect on reverberation time of changing the distribution of absorption, keeping the surface average alpha bar of alpha (P) constant.