Mean-free-paths in concert and chamber-music halls and validation of the Sabine/Eyring equations for predicting their reverberation times

Abstract

The Eyring/Sabine equations assume that in a large irregular room a sound wave travels in straight lines from one surface to another. It is assumed that the surfaces have an average sound absorption coefficient αav and that the average distance between reflections, i.e., the mean-free-path MFP, is 4V/Stot where V is the volume of the room and Stot is the total area of all of its surfaces. No account is taken of diffusivity of the surfaces. The 4V/Stot relation is based on experimental determinations in 11 very differently shaped rooms made by Vern Knudsen [Architectural Acoustics, (Wiley, 1932), pp. 132–141]. This paper sets out to test this relation experimentally for a wide variety of unoccupied concert and chamber music halls with seating capacities ranging from 200 to 15,000. To determine the MFP’s in them, the measured values of the sound strengths G and reverberation times RT were used. Computer simulations of the sound fields for several of these rooms were also made to determine the MFP’s. For these rooms, 4V/Stot is found to be an acceptable relation for MFP in the Sabine/Eyring equations.