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

Abstract

This paper builds on earlier work by the same authors to derive expressions for the time-averaged acoustic energy density in the frequency domain using the auto- and cross-spectral densities of multiple microphone elements. Expressions for the most common three-dimensional geometric arrangements are derived. Simplified expressions for use with two channel spectrum analysers are also presented.

Statistical properties of kinetic and total energy densities in reverberant spaces

“…6 However, until recently measurement of the total sound energy density has required an elaborate arrangement based on finite-difference approximations using at least four pressure microphones. [6][7][8][9] The microphones should be amplitude and phase matched very well, and the signal-to-noise ratio is poor because the finitedifference signals should be time integrated, 10 which is perhaps one of the reasons why the method has not been used much in practice. With the advent of a three-dimensional particle velocity transducer, "Microflown," 11 it has become somewhat easier to measure kinetic and total rather than only potential energy density in a sound field, as demonstrated a few years ago.…”

Comparison of methods for processing acoustic intensity from orthogonal multimicrophone probes

“…When the pressure is estimated this way in conjunction with the three points velocity estimate the orthogonal probe is essentially being used as three one-dimensional probes, such as the probe used by Vandenhout et al 19 However, it was found that when using the three points velocity estimate this pressure estimate is equivalent to using the pressure estimate in Eq. (13). This is a non-obvious result, and is proven mathematically in the Appendix.…”

“…(3) is used. 13 The Taylor expansion for collocating velocity estimates, as described previously, leads to a new method for estimating pressure. A Taylor expansion of the measured pressures can be used to estimate the pressure at (h, h, h), collocated with the velocity estimates.…”

“…1(a), the orthogonal design consists of one microphone at an "origin" position (labeled microphone 1) with the other three microphones (labeled 2-4) equidistant from the first microphone along the three coordinate axes. It has previously been referred to as the "cubic" probe, 13,14 but "orthogonal" is preferred here because the probe does not consist of microphones at all the vertices of a cube.…”

Advances in active control of machinery and device noise

“…Another approach for enlarging the zones of quiet is to minimize the total acoustic energy density. It requires measuring or estimating sound particle velocity [10], [12], [13]. Unfortunately, the sensors are extremely expensive and large.…”