Frequency‐Correlation Functions of Frequency Responses in Rooms

A mathematical study of the random interference of sound waves in large rooms requires statistical methods. “Statistical wave acoustics” is based on the random interference of many simultaneously excited normal modes of a room. In general, the random interference takes place for frequencies above 2000 (T60/V)12, where T60 is the reverberation time (in sec) and V is the volume (in m3) of the room. In the statistical theory, frequency responses between two points in a room are treated as random functions. The probability distributions, correlation functions, and “spectra” of these random functions are determined by physical parameters such as the distance between source and receiver, the volume and reverberation time of the room (or distribution of reverberation times), etc.In this paper, correlation functions of frequency responses are derived for rooms with uniform reverberation time, and negligible direct sound transmission between source and receiver. Analytic formulas for the following frequency correl...