Surface roughness in reverberation.

Sabine, Eyring, and others derived approximate formulas for the reverberation time of sound dying out in a room. These formulas use a single coefficient to take account of surface absorption, but ignore the way directions are assigned to reflected sound rays. However Joyce's exact treatment of a spherical room showed that rooms with diffuse reflection and with nearly specular reflection had significantly different reverberation times. Here two more examples show the effect of changing the reflection law. The rooms now reflect specularly at some points and diffusely at others. Large differences in reverberation time are found for a dome-shaped room. Only small differences are found for a diffuse sphere containing a smaller sphere that can be either diffuse or specular.