Expression for the estimation of time-averaged acoustic energy density using the two-microphone method.

Acoustic energy density has been shown to exhibit lower spatial variance in reactive sound fields compared to the acoustic potential energy estimate offered by microphones, making it a very useful measure of the acoustic energy within an enclosure. Previously, frequency-domain time-averaged energy density estimates have come about by estimating the pressure-average and particle velocity between two closely spaced microphones using either analog or digital electronics. A frequency domain expression can be obtained by adding the weighted sum of the auto-spectral densities of both the pressure and particle velocity magnitude. The purpose of this paper is to derive an expression for the time-averaged acoustic energy density in the frequency domain using the autoand cross-spectral densities between the two closely spaced microphones. The resulting expression is validated numerically.