Acoustics of small rectangular rooms: Analytical and numerical determination of reverberation parameters

A small rectangular room with hard walls has a number of acoustic flaws and the most serious drawback is a long reverberation time. A technique commonly used for improving room acoustics consists in increasing a sound absorption on a ceiling. In this study, the impact of acoustical treatment of a ceiling on reverberant properties of a small rectangular room was examined. Changes in the modal reverberation time due to this treatment were investigated by the analytical method. As was evidenced by calculations, the initial increase in a sound absorption on a ceiling causes a substantial decrease in the modal reverberation time and a treatment efficiency decreases with a further absorption increase. It was found also that for a room with hard walls statistical and wave theories give the same result as the modal reverberation time for oblique modes and the Sabine's reverberation time are identical. A more detailed information about reverberant properties of a room was provided by the numerical method employing a backward integration of the squared room impulse response. Using this method, global and local reverberation parameters were determined. Numerical simulations discovered a quite good agreement between global and local reverberation time and high differences between global and local early decay time resulting from a nonlinear shape of a decay curve. Therefore, one can conclude that the global decay times characterize reasonably well a reverberation process in a late stage of sound decay but they are not correctly describe this process in an initial stage.