Perturbation of Sound Waves in Irregular Rooms

Abstract

A recently developed boundary perturbation theory is applied to the solution of certain problems in room acoustics. Wave patterns and normal frequencies can be calculated for rooms having walls which are distorted by shape irregularities, by non-uniformities of boundary absorption, or by a combination of these. The method is quite general; it is applicable to any form of irregularity if the amount of distortion is “small,” provided solutions for the basic form are obtainable. Specific formulas are derived for trapezoidal shapes and calculations agree closely with experimental patterns and frequencies reported previously. An experiment has been devised to test the range of validity of the perturbation formulas for one case. A small test chamber was built with walls which could be shifted continuously in plan to give trapezoids of constant area, having any desired degree of deformity. A number of normal frequencies were traced through the whole range of shapes. For wall angle shifts up to about 15° the perturbation calculations hold well. The perturbation theory yields certain general conclusions regarding the problem of sound diffusion in irregular rooms. These appear to be of particular interest in the light of recent experience in applied acoustic design.