Precision of active sound intensity measurements in a progressive and a nonprogressive field

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Abstract
The estimated sound intensity is compared to the exact intensity in order to study the precision of active sound intensity measurement, for the cases of a simple progressive field and any sort of nonprogressive fields. The progressive field is produced by an harmonic monopole, whereas the nonprogressive field is produced by two harmonic monopoles of variable strength ratio and geometric conditions. The analysis is performed in the time domain. In the progressive field case, a general formulation of the error is obtained which simplifies in limiting cases to forms already published in the literature. In the nonprogressive field case, emphasis is put on the formulation of the exact phase gradient and of the total pressure field resulting from the two sources. The formulation of the uncertainty points out considerable errors at low frequencies due to instrumental phase mismatch and at high frequencies due to finite approximation of amplitude and of the phase gradient. Finally, the ratio of the sound intensity to the pressure as an indicator of the accuracy of sound intensity measurement is discussed.

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