Fluctuations of Sound with Position in a Reverberant Room

Abstract

Spatial fluctuations of sound in reverberant rooms are examined theoretically for the case of a fixed source and movable receiver. The approach is to describe statistics of the time-averaged squared sound pressure, as a function of frequency. These statistics apply to reverberant rooms at high frequencies, such that the modal overlap (ratio of modal bandwidth to the average spacing between modes) is larger than about 3, and for regions sufficiently removed from the source that the reverberant field prevails. Within these bounds of frequency and space, squared sound pressure may be profitably viewed as a stochastic process over frequency. At each frequency in this range, squared sound pressure is a random variable obeying an exponential probability law over space. The family of random variables obtained by considering all frequencies in this range defines a stochastic process. The process is employed to derive formulas for the spatial variance of squared sound pressure for the cases of single tone, multitone, warbletone, and narrow-band noise excitation. Experimental confirmation and suggested applications are given in many instances. In general, the variance is small when the product of bandwidth and reverberation time is large, as long as reverberation time is not so large as to prevent high modal overlap.