Functional-differential-equation models of reverberant energy decay in systems of coupled rooms

Abstract

Statistical-acoustics (SA) models of reverberant energy decay in systems of coupled rooms conventionally represent energy densities of subrooms as solutions of systems of coupled ordinary differential equations. These models unrealistically assume that exchange of energy between subrooms is instantaneous. Lyle has proposed a functional-differential-equation (FDE) SA model in which travel time of energy between subrooms is incorporated as constant delay times estimated from distances between centroids of adjacent subrooms [C. D. Lyle, Acoust. Lett. 4, 248–252 (1981)]. Here, an FDE-SA model is proposed which more generally accounts for travel-time distributions and, further, incorporates previously introduced improved decay models within subrooms [J. E. Summers et al., J. Acoust. Soc. Am. (in press)]. Monte Carlo methods are used to estimate travel-time distributions for simple geometries and allow for predictions with the FDE-SA model. Comparison of scale-model measurements and predictions of a computational geometrical-acoustics model with those of SA models shows that, contrary to Lyles findings, FDE-SA models must consider more than first moments of travel-time distributions in order to yield more accurate predictions. [This work was supported by the Bass Foundation.] a)Current address: Acoustics Division, Naval Research Lab, Washington, DC 20375-5350.