Boundary element prediction of steady-state broadband interior sound fields using absorption-based scaling

Abstract

Energy-intensity boundary elements are used in combination with the method of absorption-based scaling to predict steady-state broadband sound fields in enclosures with diffuse reflection boundaries. The wall absorption is expressed in terms of an overall absorption parameter—the spatially averaged value—and spatial variations around this mean. Boundary element strengths are expressed in a power series of the overall absorption, treated as a small parameter, thereby giving a separate problem at each order. The first problem has a uniform mean-square pressure proportional to the reciprocal of the absorption parameter. The second problem gives mean-square pressure and intensity distributions that are independent of the absorption parameter and are primarily responsible for the spatial variation of the reverberant field. This problem depends on the location of sources and the spatial distribution of absorption, but not overall absorption. Higher order problems proceed in powers of the absorption parameter, as corrections to the primary spatial variation. Boundary element solutions are obtained for each order, and the simplest model for spatial variation gives fairly accurate predictions. The method gives physical understanding of the causes of the spatial variation of enclosure sound fields and provides specific insights into the behavior and design of acoustic spaces.