Modeling Non-Diffuse Sound Fields in Room Acoustics: From Murray Hodgson’s Early Works to The Diffusion Equation Model - Valeau, Vincent; Foy, Cédric; Picaut, Judicaël (Canadian Acoustics, 2019)
The concept of diffuse sound field in room acoustics is the basic assumption of the classical theory or reverberation. This assumption is however false in many practical situations where the reverberant sound field undergoes significant spatial variations in the room. Murray Hodgson has dedicated an important part of his research activities to the study of such non-diffuse sound fields, through studies combining generally both experimental and modeling aspects. Some of Hodgson’s early contributions in link with this topic are first presented. In a second part, the paper presents some developments concerning a statistical model of non-diffuse sound fields based on a diffusion process. The paper focuses in particular on the modeling of mixed reflections within this diffusion model, the application of this model to industrial workrooms, and the modeling of energy flows by using the Fick’s law. All these developments are a natural continuation of Hodgson's work, concerning numerous issues that he raised on the modeling of non-diffuse sound fields.