Expression for the estimation of time-averaged acoustic energy density using the two-microphone method (L)

Abstract

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 letter 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.

Frequency domain expressions for the estimation of time-averaged acoustic energy density

“…The analytical derivation in this paper closely follows the derivation by Ghan et al 3 The instantaneous acoustic energy density, E D (t), at a point is defined as the sum of the acoustic potential energy density and the acoustic kinetic energy density at that point, given by 6…”

“…If the six microphones are mounted in a rigid sphere as described by Parkins et al, 8 then the substitution hϭ 3 2 r should be made, where r is radius of the sphere.…”

Statistical errors in the estimation of time-averaged acoustic energy density using the two-microphone method

“…11 In this paper, an expression for the normalized random error of this estimate is derived. The method here is similar to that used to derive the normalized random error in the estimation of sound intensity.…”

Modeling the acoustic radiation force in microfluidic chambers

“…Also, a useful figure of merit for evaluating design performance is the time averaged energy density of the fluid region, which requires estimates for the pressure and velocity fields in the fluid. 9 A generalized formulation for the energy density and the radiation force fields in two-and threedimensional geometries is developed.…”