  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.
