The scattering of acoustic waves from three-dimensional compressible fluid scatterers is considered. Particular attention is paid to cases where the scatterers have moderate magnitude in compressibility contrast and nondimensional wave number. The perturbation method based on Padé approximants developed by Chandra and Thompson [J. Acoust. Soc. Am. 92, 1047–1055 (1992)] is extended to allow the solution of problems in three dimensions. It is shown that the functional form afforded by the Padé approximant model allows one to represent and evaluate the characteristic resonances and mode shapes of the scattered pressure field. These modes are a function of the compressibility contrast and the frequency of the incident pressure wave. Numerical results are shown to compare favorably with analytical solutions for scattering from a sphere. The Padé approximant method is shown to be feasible for calculating the pressure scattered from an inhomogeneous distribution of scatterers as well as for determining internal resonance.
Frequently the results of time-varying computer simulations of acoustic behavior in built environments are difficult to analyze due the multidimensional nature of the numerical results. Graphical displays of acoustic data have been effective in remedying this problem. A technique for visualizing the time evolution of a sound pressure field within an enclosure due to a source located in the enclosure is presented. The numerical technique for computing the pressure distribution within the enclosure employs the method of images. Padé approximants are used to take into consideration the effects of sound scattering under high-contrast conditions. The graphical representation of the enclosure is created as follows. The walls of the enclosure and objects contained therein are rendered with the standard radiosity method. The graphical display of the interaction of the pressure field with the enclosure and its contents was accomplished by rendering each volume element in the field according to the pressure magnitude. The presentation will include a sequence of images depicting the time evolution of the pressure field in the enclosure.
A numerical simulation and visualization of time-varying pressure fields in inhomogeneous fluid media is considered. Medium inhomogeneities considered included attenuation, compressibility, and density contrasts. Of particular interest is the analysis of scattering from anisotropic media and the corresponding directional characteristics of the scattered field. The simulation model is based on a Padé approximant representation for the pressure. This model allows the computation of scattered fields at size parameters ka∼O(1). A finite set of wave-number responses is obtained by a solution of Green’s integral equation. The temporal response is obtained by inverse Fourier transformations of the wave-number response modulated by the incident field. Visualization techniques are developed to track strong scattering directions and to identify optimum measurement surfaces. [Work supported in part by and AT&T Bell Laboratories Cooperative Research Fellowship.]
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