Bias error comparison for plane-wave acoustic intensity using cross-spectral and phase-and-amplitude-gradient-estimator methods

Abstract

Acoustic vector intensity relies on the product of the acoustic pressure and particle velocity. The particle velocity is typically approximated via Euler’s equation using the gradient of the complex pressure across closely spaced microphones, which is traditionally found using the cross-spectral density. In contrast, the phase-and-amplitude-gradient-estimator (PAGE) method [Thomas et al., J. Acoust. Soc. Am., 137, 3366-3376 (2015)] relies on gradients of pressure magnitude and phase. For a broadband source this allows for the phase to be unwrapped, which extends the usable bandwidth of the intensity calculation well above the spatial Nyquist frequency. The benefits of the PAGE method are evident in plane wave tube measurements in which microphones spaced 90 cm apart yield accurate intensity values at frequencies at least ten times the spatial Nyquist frequency. This represents an increase in bandwidth of 30 times over the traditional method. The bias errors for the traditional method for calculating acoustic intensity are reviewed and compared with the bias errors for the PAGE method for the case of both two and three microphone intensity probes in a plane-wave tube environment. [Work supported by the National Science Foundation.]