A systematic method to obtain 3D finite-difference formulations for acoustic intensity and other energy quantities

Experimental validation of acoustic intensity bandwidth extension by phase unwrapping

“…21 Because the dominant acoustic radiation occurs at !3 kHz, the PAGE method is essential in obtaining accurate acoustic intensity measurements. The slight separation of L P and L I below 2 kHz at locations I and II is likely caused by some combination of acoustic near-field errors-both in calculating large gradients with a first-order least-squares estimate 9,13 and because the near-field intensity is likely a superposition of radiated and hydrodynamic pressure fluctuations. 22 These lowfrequency effects are important physically and are the subject of on-going investigations, but are not central to this letter's core message.…”

“…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. Recently, the challenge of characterizing jet noise fields 10,11 motivated formulation of a new intensity calculation method that extends multimicrophone probes' bandwidth.…”

Intensity analysis of the dominant frequencies of military jet aircraft noise

“…16 According to the tetrahedral probe geometry, the various cross-spectral components were weighted and summed to give intensity components along the three cardinal directions using the least-squares technique developed by Pascal and Li. 17 The resulting single-frequency intensity vectors are plotted, as in Fig. 6, at the measurement locations along plane 2 (see Fig.…”

Statistical properties of kinetic and total energy densities in reverberant spaces

“…6 However, until recently measurement of the total sound energy density has required an elaborate arrangement based on finite-difference approximations using at least four pressure microphones. [6][7][8][9] The microphones should be amplitude and phase matched very well, and the signal-to-noise ratio is poor because the finitedifference signals should be time integrated, 10 which is perhaps one of the reasons why the method has not been used much in practice. With the advent of a three-dimensional particle velocity transducer, "Microflown," 11 it has become somewhat easier to measure kinetic and total rather than only potential energy density in a sound field, as demonstrated a few years ago.…”