Evaluation of the phase error in sound intensity measurement

Abstract

This paper presents an analysis of phase dependencies occurring in investigations of sound intensity, in particular those of the effect of the phase error of measurement equipment on the value and direction of the intensity vector measured at some point. Two methods of intensity measurement, based on measurement of the particle velocity from the pressure gradient, were taken into consideration: the direct method (formulae (5), (10), (12), (13)) and the one based on the cross-spectrum of acoustic pressure signals (formulae (6), (23)). The phase error Δφ causes changes in the directional characteristic of the system (formula (28), Fig. 7), changes in the values of intensity, measured with changed order of the measurement channels (formula (30), Fig. 6), the ratio of the values of the real part of the cross-spectrum of the pressure processes from the two microphones to that of its imaginary part (Figs. 9-10), and also in the existence of the imaginary part of their cross-spectrum when the two microphones are affected by the same acoustic field (formula (42), Fig. 8). This paper presents theoretical considerations and specific examples of phase error evaluation in equipment used in investigations (Fig. 1) on the basis of the changes in question, which cause it. The phase error of equipment causes considerable distortion of results, involving changes in the measured values, direction and also the sign of the intensity vector in some cases (see Fig. 11), therefore it is important to interpret it correctly.