Comparison of multimicrophone probe design and processing methods in measuring acoustic intensity

Abstract

Three multimicrophone probe arrangements used to measure acoustic intensity are the four-microphone regular tetrahedral, the four-microphone orthogonal, and the six-microphone designs. Finite-sum and finite-difference processing methods can be used with such probes to estimate pressure and particle velocity, respectively. A numerical analysis is performed to investigate the bias inherent in each combination of probe design and processing method. Probes consisting of matched point sensor microphones both embedded and not embedded on the surface of a rigid sphere are considered. Results are given for plane wave fields in terms of root-mean-square average bias and maximum bias as a function of angle of incidence. An experimental verification of the analysis model is described. Of the combinations considered and under the stated conditions, the orthogonal probe using the origin microphone for the pressure estimate is shown to have the lowest amount of intensity magnitude bias. Lowest intensity direction bias comes from the six-microphone probe using an average of the 15 intensity components calculated using all microphone pairs. Also discussed are how multimicrophone probes can advantageously use correction factors calculated from a numerical analysis and how the results of such an analysis depend on the chosen definition of the dimensionless frequency.

Experimental validation of acoustic intensity bandwidth extension by phase unwrapping

“…5 A limitation of using multimicrophone intensity probes 6 to characterize broadband sources and fields has been a requirement of repeating the measurement with a number of microphone spacings to overcome the significant bias errors 7 associated with the traditional quadspectrum-based intensity method. 8,9 This process increases measurement time and cost.…”

Phase and amplitude gradient method for the estimation of acoustic vector quantities

“…The work of Wiederhold et al 28,29,34 gives a detailed analysis of optimal methods of finding p 0 given different probe configurations. In these works, Wiederhold et al discuss different finite-sum and -difference processing methods and their associated biases.…”

“…These include low-frequency phase mismatch, 20 high-frequency probe performance, 21 and the effect of scattering bias, 22,23 as well as the design of multidimensional probes. [24][25][26][27] In recent papers, Wiederhold et al 28,29 reviewed many probe designs and considered different schemes for optimal estimation of sound intensity using the FD method. The foundation for all of these studies is the original FD method, which involves sums and differences of complex pressures or cross spectra.…”

Development of a Near-field Intensity Measurement Capability for Static Rocket Firings

“…3,7,8) The idea of a multimicrophone probe within a rigid sphere was based on prior work [12][13][14] and prompted a number of complementary investigations to further quantify its performance. [15][16][17] Seen in Fig. 4, the 2.54-cm diameter sphere contains four flush-mounted, externally polarized G.R.A.S.…”

“…20) The pressure is obtained from a centered microphone (as with the 2D probe) or estimated via an average of the other microphones, which was the subject of Wiederhold et al's work. 15,16) The particle velocity is obtained a finite difference estimate of the pressure gradient and the time-harmonic version of the linearized Euler's equation for an inviscid acoustic process, written as…”