Pertinence of a simplified plane wave model for reverberation energy decays in rooms with a pair of parallel surfaces

An analytical model has been developed recently to take into account specular and diffuse reflections in rooms with a pair of parallel surfaces. Analytical models can help to better understand the influence of scattering coefficients’ values in those rooms in which unusually long reverberation times can be created by locked-in rays. Also, analytical models can be used complementary to ray-tracing methods to quickly estimate the late part of reverberation decays. The developed model is based on the formalism of sound particles emitted in the room by a point isotropic source. Some approximations lead to an intuitive analytical model including the influence of absorption and scattering coefficients on reverberation. The purpose of this paper is to develop and analyse the pertinence of an additional simplification to the model, based on the assumption of plane waves propagating between the two parallel walls. In this case, the model predicts a reverberation in the room composed of two exponential decays. The pertinence will be analysed by comparing this simplified plane wave model with reverberation decays computed by a sound ray program.