Acoustical scattering from multiple spheres by using a kind of addition formulae for the spherical wave functions

A kind of addition formulae for the spherical wave functions is generated first by using the bicentric expansion of Green function in spherical coordinates. For an acoustic system with multiple spheres, the addition formulae permit the field expansions all referred to the center of one of the spheres, whose boundary conditions can be consequently used to study the acoustic scattering from multiple spheres easily. The two-sphere acoustic system with different boundary conditions is considered and the scattered field by each sphere can be obtained by solving an infinite set of two linear, complex, algebraic equations, whose coefficients are coupled through double sums in the spherical wave functions. Finally, the form functions of two spheres insonified by plane waves at arbitrary angles of incidence are calculated and the addition formulae generated are validated by comparing the corresponding numerical results with those of the existing literature.