A Mathematical Model of Diffuse Sound Field Based on a Diffusion Equation

摘要

A natural extension to the concept of diffuse sound field based on the mathematical theory of diffusion is proposed, and the uniformity of the sound density and the energy flow is discussed. Indeed, the analogy between a sound particle hitting walls and a single particle moving in a gas and hitting scattering objects shows that the sound density in a room follows a diffusion equation. Beside the reverberation time defined in the traditional theory of diffuse sound field, a new parameter, the diffusion coefficient, is introduced. One-diraensional solutions for rectangular enclosures with diffusely reflecting walls are given and compared to a numerical simulation of diffuse sound field derived by Kuttruff: a good agreement is observed.