Abstract
A new analysis of high-frequency broadband reverberant sound fields in rooms with diffuse reflection boundaries is described. Depending on shape, source location, and distribution of wall absorption, rooms exhibit spatial variation in steady-state mean-square pressure and also spatial dependence of decay time characteristics. 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. The mean-square pressure field is expressed as a sum of constituent modes. The intensity field, which is related to the pressure field in a complex way, can be calculated for each mode. Boundary conditions relate averaged intensity and pressure. The mean-square pressure is expressed in terms of the modal sum. Lower order modes are responsible for the overall smooth spatial variation in the reverberant field; higher modes account for more rapid local variations near walls due to changes in wall properties. In the transient problem, the spatial eigenmodes decay at different rates, leading to a spatial redistribution of reverberant energy, and causing the decay curves to be a function of position in the room. Sample calculations and comparisons with other solution methods are presented.
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