Prediction of broadband sound fields in enclosures by decomposition in powers of an absorption parameter

A novel analysis for steady-state or time-dependent broadband diffuse sound fields in enclosures is developed. Beginning with a formulation utilizing broadband intensity boundary sources, the strength of these wall sources is expanded in a series in powers of an absorption parameter, giving a separate boundary integral problem for each power. The first problem has a uniform interior level proportional to the reciprocal of the absorption parameter, as expected. The second problem gives a mean-square pressure distribution that is independent of the absorption parameter and is 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 the overall absorption level. Additional problems proceed at integer powers of the absorption parameter, but are essentially higher order corrections to the spatial variation. The important second problem and the higher order problems are easily solved numerically on a one-time basis for a given distribution of absorption and given source locations. Solutions show the method to be accurate and efficient for the prediction of the reverberant and overall pressure fields. The approach gives physical insight into the primary effects governing spatial variations in broadband sound fields.