Acoustic Radiation from a Pair of Spheres

In this paper we present a semi-analytical model which enables the acoustic pressure field created by two spheres radiating close together to be predicted at any point outside the spheres. By representing the pressure field from each sphere as a finite sum of spherical harmonics and satisfying the boundary conditions at a finite number of points on the surface of each sphere, the problem reduces to the solution of a system of simultaneous linear equations whose unknown variables are the relative amplitudes of each spherical harmonic. The results from this model have been compared with those obtained using a boundary element method approach. It is shown that for values of ka < 10 both methods give results with a relative error less than 1% for separated spheres. The case for contacting spheres is discussed and results presented. Numerical examples demonstrate the accuracy and convergence rates of the two methods. A detailed analysis of the radiation problem when the spheres are in contact is given in an Appendix.