Modeling the inhomogeneous reverberant sound field within the acoustic diffusion model: A statistical approach

In room acoustics, starting from the sound particle concept, it is now well established that the reverberant field can be modeled from a diffusion equation function of the acoustic density and a gradient equation function of the acoustic intensity. The main works on the development of an acoustic diffusion model have highlighted the major role of a coefficient of the model, the so-called diffusion coefficient. Indeed, the main phenomena influencing the reverberant sound field can be modeled by proposing an appropriate expression of this diffusion coefficient. The work presented here deals with the modeling of inhomogeneous reverberant sound fields induced by geometric disproportions, and investigates, in particular, the case of long rooms. Previously, the ability of the acoustic diffusion to model adequately the spatial variations of the sound field along the room has been demonstrated by considering a diffusion coefficient that is spatially dependent. We propose here to extend this work by determining an empirical law of the diffusion coefficient, depending on both the scattering and absorption coefficients of the walls of the room. The approach proposed here is statistical and is based on the least squares method. Several linear models are proposed, for which a rigorous statistical analysis makes it possible to assess their relevance.