Theoretical model of reverberation decay in a rectangular room—Potential for predicting flutter echo

Abstract

Reverberation is the most important factor governing the acoustic design of a room. It is known that non-exponential reverberation decay may occur in a room with unevenly distributed sound absorption, namely, with non-diffuse sound field. We propose the theoretical model of reverberation decay in non-diffuse sound fields. The reverberation decay is characterized by absorption and scattering properties of the surfaces of a room. As a first step for developing reverberation theory of non-diffuse sound field, the proposed model deals with rectangular rooms, because rectangular rooms are very common in any kind of buildings and architecture. Spatial absorption coefficients for three orthogonal directions are defined as the parameters which characterize the energy decay curve in the rectangular room. Within this model, the reverberation in such rectangular room becomes a combination of exponential and power law decay. The power law dependence as a function of time has a singularity. This issue is resolved within the model. The model was verified by comparison with the results of computer simulation using sound ray tracing method. Theoretical solutions of the proposed model agree well with the results of the computer simulation. Potential for predicting flutter echo by this model is also discussed.