根据Kirchhoff-Helmholtz声衍射理论，独立推导了沿抛物面镜轴线的球面波反射声场的时域理论解。基于理论解预测近场反射波中存在三种子波，即“中心波”、“边缘波”和“尾波”，中心波的相位与边缘波和尾波相反。远场反射波与声源波形的导数形式相同，声压幅值和传播距离成反比而与声波频率成正比。以典型的正弦波为例给出了反射声场的演化形成过程，并通过COMSOL软件进行数值模拟验证了三种子波的存在及理论解的正确性。最后研究了球面波反射声场的特性，如果抛物面镜的口径固定，则存在一个最优的深焦比参数d/zF=3.92使得远场的反射波声功率密度最大。
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.
关键词
抛物面镜 /
球面声波 /
反射声场
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Key words
Parabolic mirror /
spherical sound wave /
reflection
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