A Field Equation Approach to Predict Energy and Intensity of Non-Uniform Time-Dependent Broadband Sound Fields in Enclosures with Diffuse Reflection

A new approach for the analysis of high-frequency broadband reverberant sound fields in rooms with diffuse reflection boundaries is described. Depending on shape, source location, and the distribution of wall absorption, rooms exhibit spatial variation in steadystate mean-square pressure and also spatial dependence of decay time characteristics. It is shown that the room boundaries can be replaced by a distribution of uncorrelated broadband directional energy-intensity sources. In steady state with diffuse reflection boundaries, the interior pressure field produced by these sources satisfies Laplace’s equation. This fact allows the mean-square pressure field to be re-expressed as a sum of constituent modes. The corresponding intensity field, which is related to the pressure field in a complex way, can be calculated in closed form for each of these modes. Wall boundary conditions relate the intensity and pressure fields. The mean-square pressure solution is expressed in terms of the modal sum. The lower order modes are largely responsible for the overall smooth spatial variation in the reverberant field, and the higher order modes account for more rapid local variations near walls due to changes in wall properties. In the transient problem the eigenmodes decay at different rates, leading to a spatial redistribution of reverberant energy once the source is turned off, and causing the decay curves to be a function of position in the room. Sample calculations are presented.