Diffusion-based models for predicting sound fields in rooms with mixed specular and diffuse reflection

A diffusion model, based on the numerical solution of a diffusion equation, was developed in the past to give accurate predictions of the sound-pressure level and of the sound decay at any location in a single enclosure or in coupled rooms. However, this model is limited to rooms with diffusely reflecting walls. In this study, two methods are presented to extend this model to rooms with mixed specular and diffuse reflections, defined by the classical room-acoustics scattering coefficient. The first method models the reverberant field by using a modified diffusion process, with an empirical diffusion constant departing from the theoretical one based on the mean free path. The set of these coefficients, which depend on the scattering coefficient, has been found empirically to fit the results given by a ray-tracing program. The second method is a hybrid approach. The reverberant sound field due to the diffuse reflections is first obtained with the original diffusion model. Then the sound field due to the specular reflections is modelled with an image-source model. The results given by the two approaches are compared to experimental data obtained for several types of rooms (a classroom, an office and some long rooms).