Analysis method for temporal decay of diffuse broadband sound fields in enclosures

Abstract

An analysis method to predict the behavior of time-dependent broadband diffuse sound fields in enclosures is described. A formulation utilizing time-dependent broadband energy-intensity boundary sources, including propagation time delays, is developed as a numerical boundary element method. An interpolation method is used to re-express the actual delays in terms of a discrete set of integer-multiple delays, thereby facilitating the numerical solution. The method is demonstrated for the prediction of temporal decay in interconnected one-dimensional channels and in two-dimensional enclosures. Temporal behavior is expressed in terms of a higher-dimensional eigenvalue/eigenmode problem, with boundary source strength distributions expressed as eigenmodes. In temporal decay from steady state, solutions exhibit rapid short-time spatial redistribution of energy, followed by long-time decay of a predominant spatial eigenmode. Long-time decay depends on behavior of the most slowly decaying eigenmode and the relative source-panel strengths do not depend on initial conditions. Short-time adjustment and decay depends on initial source characteristics and the relative distribution of absorbing material. An interesting feature of the short-time behavior is that the time-decaying eigenmodes are primarily a manifestation of energy redistribution rather than absorption.