Jean-Dominique Polack (LAM)

Revisiting reverberation

In 1992, the author proposed a generalisation of Sabine 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  presentation revisits this development and justifies it with the help of free path statistics in ergodic 2D and 3D circular and rectangular enclosures. It proves that all  reverberation formula can be reduced to the general formula, provided integration is properly processed, leading to formulas that never diverge. The presentation  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, thus improving reverberation time prediction. Lastly, the approach is  extended to non-ergodic enclosures.