Optimized vector sound intensity measurements with a tetrahedral arrangement of microphones in a spherical shell

Abstract

Recent times have seen the introduction of small spherical arrays whose usefulness as sound intensity probes is the focus of this paper. The presented probe consists of a spherical shell, 30 mm in diameter, housing four 14 in. microphones arranged in a regular tetrahedral configuration. Classical formulae may be used to estimate the sound intensity vector, as may methods based on spherical harmonics decomposition. Results are shown to be comparable to those obtained from classical sound intensity probes. The existence of an analytical model for a plane wave's diffraction about a sphere provides a means for adopting common optimization techniques for potentially improving the intensity vector estimate, however. This paper examines the validity of non-linear least squares optimization in conjunction with the proposed spherical sound intensity probe when placed in the following sound fields: (1) a simple plane wave; (2) a plane wave corrupted by noise; and (3) multiple incident plane waves. Under certain conditions, the probe is shown to greatly extend the operational frequency range of classical sound intensity probes. The optimization algorithm is found to lack robustness against deviations from plane wave conditions, however.