Explanation of direction finding with a vector sound-intensity probe

Abstract

An explanation is provided of direction finding with a vector sound-intensity probe in the far field of a single sound source. As described earlier [Hickling etal., J. Acoust. Soc. Am. 94, 2408–2412 (1993)], the probe consists of four pressure sensors in the tetrahedral arrangement, intensity being measured with the cross-spectral method. The probe has omnidirectional sensitivity. Direction-finding with an arrangement of pressure sensors makes use either of beamforming or of differences in phase, time-of-arrival or amplitude at two sensors. It is shown that direction finding with the vector probe is based on phase differences. The close spacing of the pressure sensors of the probe relative to wavelength creates a relation between the intensity-vector components and phase that is independent of the ratio of sensor spacing to wavelength, each component being dependent only on the pressure-amplitude squared and the direction of the source. Accuracy of direction finding depends on the accuracy with which the components of the intensity vector can be measured. The accuracy of vector intensity measurement has been demonstrated a number of times. Examples are presented of the accuracy of direction finding with a vector probe in water.