The exact spheroidal-function series solution for the time-harmonic acoustic scattering of a plane wave by two fluid confocal prolate spheroids is developed and a numerical implementation is formulated and validated by independent methods. The two spheroids define three regions in which the acoustic fields are expanded in terms of spheroidal wave functions multiplied by unknown coefficients. These expansions are forced to satisfy the boundary conditions and by using the orthogonality properties of the involved functions an infinite matricial system for the coefficients is obtained. The resulting system is then solved through a truncation procedure. The implementation has no limitations regarding the sound speed and density of the three media involved or in the incidence frequency.

提出了两个流体共聚焦扁球体对平面波进行时谐声散射的精确球函数级数解，并通过独立的方法建立了数值实现并进行了验证。这两个球体定义了三个区域，在这些区域中，根据球面波函数乘以未知系数而扩展了声场。这些扩展被迫满足边界条件，并且通过使用所涉及函数的正交性，获得了系数的无限矩阵系统。然后，通过截断过程解决生成的系统。该实施方式对于所涉及的三种介质的声速和密度或入射频率没有限制。