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A Numerical Kirchhoff-Helmholtz Solution for The Reflection of Spherical Sound Wave from a Concave Parabolic Mirror

Vol 5(4)  2017

Author:Jun Zhang, Peng Chen, Zhengwu Chen and Xunnian Wang

Page Number:337 - 344

Abstract:

The spherical sound wave generated by a plasma sound source can be focused using a concave parabolic mirror. An analytical on-axis solution for the reflection of spherical sound wave from a rigid parabolic mirror was given by Zhang and Zeng (Acta Acustica United with Acustica, 2013). However, the analytical solution is valid only along the symmetric axis of the mirror, and the off-axis information of the reflection wave is unknown. In this study, a three dimensional numerical solution based on the Kirchhoff-Helmholtz formula is presented. The correctness of the solution is verified by a comparison of the on-axis evolution of a Gaussian modulated sinusoidal pulse with the corresponding analytical solution, and by Hester’s experiment results. The off-axis evolution of the reflection sound wave and the focusing effect of the parabolic mirror are discussed. The off-axis edge wave splits into two wavelets, one of which moves towards and the other moves away from the center wave and the amplitude of the wavelets are much smaller than that of the on-axis edge wave. The peak pressure of the reflection wave decreases when the observation point moves transversely away from the axis of the parabolic mirror. The −6 dB width of the acoustic beam increases as the distance from the mirror increases. And a larger depth-to-focal-length ratio of the mirror leads to a narrower acoustic beam.


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JVET Vol 2 (2014) onwards AVE Vol 1 (2002) to Vol 12 (2013) * JVET Vol 1 (2013) is equivalent to AVE Vol 12 (2013)

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