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In the three-dimensional (3-D) sound intensity measurement using four-microphone probes, there are two well-known microphone arrangements. One is arranging four microphones at the vertexes of a regular tetrahedron and the other is arranging them at the nearest four corners of a cube. In the high frequency region, these 3-D probes suffer from the same type of sensitivity reductions as do 1-D p-p probes. In this paper, formulae to obtain three orthogonal intensity components for these two types of probes are reviewed first, and their sensitivity and leakage errors are numerically discussed not only for the along-the-axis plane wave incidences but also for incidences from various directions in the 4 space. This analysis reveals characteristic differences of measurement errors of the two types of probes. Since the sensitivity and leakage errors are systematic, it is possible to correct these errors (to some degree) using the source direction information given by a real (or a numerical) measurement. A new correction method is proposed, and the effectiveness of the method is evaluated numerically. Results show that the proposed method is very effective, and the high-end of the frequency range is widened close to the limit, at which the dimension of the 3-D probe is nearly equal to the half wavelength of the incident plane wave.

Numerical evaluation of three-dimensional sound intensity measurement accuracies and a proposal for an error correction method