CIRES, University of Colorado, Physical Sciences Division, Mail Code R/PSD99, 325 Broadway, Boulder, Colorado 80305-3328, USA.
J Acoust Soc Am. 2011 Oct;130(4):EL135-41. doi: 10.1121/1.3629140.
Wave scattering by objects that are small compared to the wavelength (Rayleigh scattering) is usually studied for plane incident waves. However, knowledge of the full Green's function of the problem becomes necessary when the separation of scatterers from either an interface or each other is comparable to the scatterers' dimensions. Here, an elementary analytic solution is derived for diffraction of a spherical sound wave by a small, soft sphere. The approximate solution is obtained from asymptotic expansions of an exact solution, holds everywhere outside the sphere, and reduces to classical results due to Kelvin and Rayleigh in appropriate special cases.
当物体相对于波长较小（瑞利散射）时，通常研究平面入射波的物体的波散射。然而，当散射体与界面或彼此之间的分离与散射体的尺寸相当时，就需要了解问题的完整格林函数。在这里，推导了一个关于小软球对球面声波的衍射的基本解析解。近似解是从精确解的渐近展开式得到的，在球体外处处成立，并在适当的特殊情况下简化为 Kelvin 和 Rayleigh 的经典结果。
