Steady state acoustic radiosity for the prediction of sound pressure levels in enclosures with diffuse surfaces

Abstract

This paper presents a derivation for and shows practical application of the steady-state diffuse acoustic radiosity method to the prediction of steady state sound levels in rooms. The paper begins with a brief review of the general radiosity literature and a more thorough review of the radiosity method in acoustics and proceeds to derive the general steady state acoustic rendering integral equation applicable to radiative energy exchange enclosures with arbitrary surface reflection properties. The rendering equation is simplified assuming diffuse reflections and the enclosure surface is discretized to convert the integral equations into summations. A closed form matrix solution to the discrete equations and another matrix equation for computing mean square pressure at multiple locations from multiple sources are presented. The computer code used for further analysis is verified by comparison to a closed form solution for a special case. Convergence of the discretized solution is investigated and the method is shown to converge linearly as the patch size decreases. A practical implementation of the method for predicting of sound levels in a classroom is shown. Predictions using radiosity are compared with simple diffuse field theory and measurements of an actual room. The radiosity method is shown to match diffuse ray tracing to within a fraction of a dB and predictions with a discretization with patches as large as 2 m are shown to be within a fraction of a dB of the asymptotic values