Bliss D., Rouse J., Franzoni L.

An absorption based analysis method is developed for steady-state broadband sound fields in enclosures having diffuse or specular reflection boundaries. The wall absorption is expressed as an overall spatially-averaged value, with spatial variations around this mean. Interior pressures and intensities 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 level proportional to the reciprocal of the absorption parameter, as expected. The second problem gives a mean-square pressure and intensity 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 absorption level. Higher order problems proceed at powers of the absorption parameter, but are essentially small corrections to the primary spatial variation. The primary spatial variation problem is solved using two different methods: modal analysis for specular reflection, and energy-intensity boundary element for diffuse reflection. Although formally developed based on treating absorption as a small parameter, the method is demonstrated to work remarkably well in practice up to large absorptions, and to provide insight into the behavior and design of acoustic spaces.