Mean-free-paths in concert and chamber music halls and the correct method for calibrating dodecahedral sound sources

The Eyring/Sabine equations assume that in a large irregular room a sound wave travels in straight lines from one surface to another, that the surfaces have an average sound absorption coefficient αav, and that the mean-free-path between reflections is 4 V/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 4 V/Stot relation was originally based on experimental determinations made by Knudsen (Architectural Acoustics, 1932, pp. 132-141). This paper sets out to test the 4 V/Stot relation experimentally for a wide variety of unoccupied concert and chamber music halls with seating capacities from 200 to 5000, using the measured sound strengths Gmid and reverberation times RT60,mid. Computer simulations of the sound fields for nine of these rooms (of varying shapes) were also made to determine the mean-free-paths by that method. The study shows that 4 V/Stot is an acceptable relation for mean-free-paths in the Sabine/Eyring equations except for halls of unusual shape. Also demonstrated is the proper method for calibrating the dodecahedral sound source used for measuring the sound strength G, i.e., the reverberation chamber method.