Theoretical study of the focusing of spherical sound wave using a parabolic mirror

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Journal of Vibration and Shock ›› 2016, Vol. 35 ›› Issue (17) : 127-133.

ZHANG Jun 1 CHEN Peng1 CHEN Zhenwu1 ZHAO Yun2 ZENG Xinwu 2

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Abstract

Based on the Kirchhoff-Helmholtz diffraction theory, a transient axial solution for the reflection of a spherical acoustic wave from a parabolic mirror was derived. It’s assumed that the wavelength is small compared to the dimension of the mirror and the geometric acoustic theory can be applied. The theoretical solution indicates that the near field reflection wave consists of three parts, i.e., the center wave, the edge wave and wake wave. The phase of the center wave is opposite to the edge wave and wake wave. The far field reflection wave is consistent with the derivative of the source waveform, and its amplitude is inversely proportion to propagation distance and in proportion to frequency. Using a sinusoidal wave as an example, the evolution and formation process of the reflection sound field is presented. The existence of three wavelets and correctness of the on-axis theoretical solution is verified by the simulation of COMSOL. Lastly, the characteristics of the reflection sound field are studied, and the effect of geometric parameters is discussed. If the aperture of the mirror is fixed, an optimum depth-to-focal-length ratio d/zF=3.92 exists which maximizes the power density of the far field reflection wave.

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Parabolic mirror / spherical sound wave / reflection

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ZHANG Jun 1 CHEN Peng1 CHEN Zhenwu1 ZHAO Yun2 ZENG Xinwu 2. Theoretical study of the focusing of spherical sound wave using a parabolic mirror[J]. Journal of Vibration and Shock, 2016, 35(17): 127-133

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