Computed Frequency and Angular-Distribution Irregularity of Normal Modes in Rectangular Rooms

Abstract

Results obtained with the computer program described in papers G5 and G6 at the 61st meeting of the Society are presented. Both frequency and angular mode spacing indices have been computed for each half-octave band over the first 4 octaves of normalized frequency for rooms with dimension ratios ranging from 313 to 1, to 1 to 1. Considerable variation in the frequency spacing criterion exists not only with changes in room dimensions but also from one half-octave band to the next, when only tens of modes are present in a band. When hundreds are present, the modes become Poisson distributed. No clearly defined optimum room dimension, as predicted by Bolt, emerges from this study. The angular distribution index is more regularly behaved with rather definite stratification apparent as a function of the room height/length ratio, when the height direction is taken as the angular reference. For rooms having satisfactory mode distribution, an approximate formula has been developed for determining the lowest midband frequency for which a room may be used for measurements of continuous spectrum sounds. The formula turns out to be a constant divided by the cube root of the volume where the constant is a function of the measuring bandwidth and the number of normal modes required therein. For 20, 12, and 9 modes in one, 12, or 13, octave bands, the constants are 1160, 1285, and 1355 cps, respectively.