Faran model solution


The “Faran model” refers to a classic solution to an imporant acoustics problem: the scattering of sound from elastic cylinders or spheres in an elastic medium under plane-wave insonification.  This model has many applications in acoustics research.

Author: M. E. Anderson
Organization: Duke University
Date posted: November 15, 1999
Code type / platform: MATLAB source / Any MATLAB platform
Use restrictions: None. (Acknowledgement requested.)
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This set of Matlab functions calculates the Faran solution for a spherical scatterer given the material properties specified by the user. Based on literature following Faran, it also extends the original solution from a monochromatic to a polychromatic (i.e. broad-band) solution. The output is complex amplitude as a function of insonifciation frequency and scattering angle.

This code uses numerical methods for portions of the solution that do not have closed-form solutions or standard Matlab function calls. Its precision provides good apparent agreement with published polychromatic solutions. Validation code is included to test the code installation and to demonstrate this agreement. The author welcomes bug reports and suggestions for refinements.

Major references:

Faran, J. J., “Sound scattering by solid cylinders and spheres,” JASA 23, pp. 405-418, 1951.

Hickling, R. H.,  “Analysis of echoes from a solid elastic sphere in water,” JASA 34, pp.1582-1592, 1962.

Example output:

(Compare to Figures 7 and 8 in Hickling.)