Revisiting reverberation formulae

Abstract

In 1992, the author proposed a generalization of Sabine's formula that develops reverberation time over a series of powers of the reflection coefficient on the boundaries. Some years later, he reduced the development to just two terms that made it possible to monitor reverberation times up to large absorptions. The present paper revisits this development and justifies it with the help of free path statistics in 3D rectangular enclosures. It proves that Kuttruff's reverberation formula is a special case of the general formula, but diverges for large absorption. Reverting to Kuttruff's original integration process leads to a formula that does not diverge. The paper further explains the difference between Eyring-type reverberation times that vanish for total absorption, and Sabine-type reverberation times that never vanish even for total absorption, and proposes a simple scheme for evaluating the asymptotic free path statistics and thus improving reverberation time prediction. Lastly, the approach is extended to non-ergodic enclosures.