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Acoustic modeling study demonstrates composite ray-mode approximations for sound scattering in gas-filled cylinders, indicating improved efficiency for fish swimbladder acoustic models.
The normal mode solution for sound backscattered by a finite fluid (gas)-filled cylinder in water is replaced by a Kirchhoff approximation for ka>0.15 and the normal mode solution for ka<0.15 where a is cylinder radius and k is the wave number. The composite solution was tested for density and sound-speed ratios g and h in the ranges of 0.0012
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Clarence S. Clay (1992) studied this question.
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