Energy flux streamlines versus acoustic rays for modeling an acoustic lens: Testing and refinement

Abstract

As an extension of recently published experimental work [Cleon E. Dean and Kendez Parker, “A ray model of sound focusing with a balloon lens: An experiment for high school students,” J. Acoust. Soc. Am. 131, 2459–2462 (2012)], preliminary results comparing energy flux streamlines [David M. F. Chapman, “Using streamlines to visualize acoustic energy flow across boundaries,” J. Acoust. Soc. Am. 124, 48–56 (2008)] versus acoustic rays for visualizing the energy flow inside and in the focal region of an acoustic lens in the form of a carbon dioxide filled balloon in air were presented. The sound field was expanded in the usual Legendre polynomials and spherical Bessel functions, and the energy flux vectors at points throughout the regions of interest were calculated [J. Adin Mann III, et al., “Instantaneous and time-averaged energy transfer in acoustic fields,” J. Acoust. Soc. Am. 82, 17–30 (1987)]. Deficiencies in the streamline plotting routines used in this earlier version of Mathematica and subtle differences between acoustic rays and acoustic energy flux streamlines lent itself to an inaccurate perception of the results. This talk uses Mathematica 10 routines to revisit these results and concentrates on testing and verification of the conclusions from the previous work.