Including the wall scattering coefficient in the diffusion model for building acoustics
Résumé
For several years, an acoustic model is developed to predict the reverberant sound field in buildings. This model is based on the idea that the propagation of the reverberant sound field obeys a transport process and, for many cases, a diffusion process that can be easily solved numerically. The work proposed here starts from the classical analytical development achieved by Feshbach and Morse in 1953, showing that a transport equation can be reduced to a diffusion equation. This model, valid in room acoustics for purely diffuse reflections, is extended in the present study to mixed reflections (with a proportion of specular and diffuse reflections, i.e. considering a scattering coefficient). The proposed mathematical developments lead to an analytical expression of the diffusion constant that is a function of the scattering coefficient, but also on the absorption coefficient of the walls. The results obtained with this modified diffusion model are then compared with the classical diffusion model, and with results obtained with a sound particle software, considering mixed wall reflections.