Acoustic cross-energy measures and their applications

Hargreaves, JA; Lam, YW

Abstract

Acoustic energy density and acoustic intensity are quantities which are well established and widely applied. When these are applied to pressure and particle-velocity fields which are the linear superposition of more than one wave they naturally separate into multiple terms; some of these involve only one of the constituent waves and others involve combinations of two waves. When one-dimensional energy measures such as covariance or power-spectral density are applied to sums of signals in this way, the terms involving only one signal are designated the ‘auto’ terms and the terms involving the combination of two signals are designated the ‘cross’ terms. This paper proposes that this terminology be extended to the acoustic energy measures, hence acoustic ‘cross-energy density’ and acoustic ‘cross-intensity’, and their physical interpretations as measures of common acoustic energy flow are discussed. It is also well known that the divergence theorem may be applied to the acoustic energy density and acoustic intensity to produce the energy flux relation; this states that acoustic energy is con-served in a volume containing a lossless medium. Here it is shown that the same may be done for the cross-energy quantities, producing an equivalent energy-flux relationship for the new cross-energy measures and showing that conservation of energy applies to these also. Furthermore it is shown that the resulting integral is equivalent to the Kirchhoff-Helmholtz Boundary Integral Equation when one of the waves is a converging spherical wave. This leads to a new energy interpretation which is also informative for other choices of waves, such as plane-waves and higher-order spherical harmonic waves. Applications of these ideas include the near-field to far-field transformation used in Finite Difference Time Domain modelling, and near-field compensated Ambisonics, where it suggests new ways to couple computer simulation algorithms to auralisation systems and new microphone array designs.

Citation

Hargreaves, J., & Lam, Y. Acoustic cross-energy measures and their applications. Presented at The 22nd International Congress on Sound and Vibration, Florence. Italy

• Presentation Conference Type: Other
• Conference Name: The 22nd International Congress on Sound and Vibration
• Conference Location: Florence. Italy
• End Date: Jul 16, 2015
• Acceptance Date: Apr 8, 2015
• Deposit Date: Feb 16, 2016
• Publicly Available Date: Apr 5, 2016
• Publisher URL: http://iiav.org/archives_icsv_last/2015_icsv22/content/papers/papers/full_paper_975_20150408142325293.pdf
• Additional Information: Event Type : Conference