Interference Patterns in Reverberant Sound Fields

Abstract

In a reverberant sound field, where at all points equal mean energy flows in all directions, it is shown that the sound energy is distributed into interference patterns the reflecting boundaries. Thus the mean energy density is not uniform at all points in the field. For a perfectly reflecting plane surface that is large compared with the wavelength, the interference pattern can be expressed as a mean squared sound pressure varying as (1 + sin2kx/2kx) where x is the distance from the surface and k is the wave number. Corresponding expressions are derived for the mean squared particle velocity and the mean energy density. The energy level at the surface is found to be 2.2 db higher than at points further away where the interference patterns are negligible. Similar expressions are derived for the interference patterns formed by two and three reflectors at right angles, as at the edges and corners of a room. The largest departure from uniformity occurs in a corner where the mean squared pressure is 9 db higher than at remote points. The effects of such interference patterns on transmission loss and reverberation room measurements are discussed briefly. The patterns are not much affected by the frequency band widths habitually used in room acoustics. Experimental confirmation of the theory is given.