The contributions of pairs of parallel surfaces in a simple analytical model of room reverberation

Abstract

In a recent paper [Embrechts, “Searching for a theoretical relation between reverberation and the scattering coefficients of surfaces in a room,” in Proceedings of the Acoustics 2012 Nantes Conference (2012), 2397–2402], we derived an analytical model of the sound energy decay in a room from the acoustic radiative transfer equation. This model includes the surfaces' scattering properties and it is presently valid for rooms in which the cloud of image sources is approximately isotropic and constant for all receptor's positions. Its validity is extended in this paper by the inclusion of a pair of parallel surfaces. Indeed, it is known that parallel surfaces can introduce significant anisotropy in the cloud of image sources. We show that the room reverberation can be represented by a sum of exponential decays (except in its early part), each decay having its specific slope and amplitude depending on the surfaces' absorption and scattering properties. It is also shown how this simple model can be applied to speed up geometrical acoustics computer simulations.