Statistical analysis of sound absorption by audience

Abstract

It is proposed that the sound absorption coefficients of acoustic materials, in general, be considered as random variables since their values depend upon the sound fields in which they are measured. This viewpoint is particularly appropriate for audience absorption since clothing, seating, etc. vary randomly. On this assumption, it is possible to decide between the classical hypothesis that the audience absorption is proportional to their number and Beranek's hypothesis that audience absorption is proportional to the occupied area, by analyzing the variance. A two-way classification of the total absorption of a number of halls is made with seating density and seating area as the row and column variables, respectively. The absorption of the hall in the ith row and jth column is written as a_ij=μ+r_i+c_j +∈_ij, where μ is the mean of all entries, and r_i and c_j are the row and column effects, respectively. The ∈_ij's represent contributions from other sources and interactions. Tests for the hypotheses r_i=0 and c_j=0 indicate that audience absorption varies significantly with seating area but not with seating density, supporting Beranek's hypothesis.