The ensemble variance of pure-tone measurements in reverberation rooms

Reverberation rooms are often used for measuring the sound power emitted by sources of sound. At medium and high frequencies, where the modal overlap is high, a fairly simple model based on sums of waves from random directions having random phase relations gives good predictions of the ensemble statistics of measurements in such rooms. Below the Schroeder frequency, the relative variance is much larger, particularly if the source emits a pure-tone. The established theory for this frequency range is based on ensemble statistics of modal sums and requires knowledge of mode shapes and the distribution of modal frequencies. This paper extends the far simpler random wave theory to low frequencies. The two theories are compared, and their predictions are found to compare well with experimental and numerical results.