An equivalent source technique for calculating the sound field inside an enclosure containing scattering objects

The equivalent source method has previously been used to calculate the exterior sound field radiated or scattered from bodies in the free-field. In this paper the method is used to calculate the internal pressure field for an enclosure which can have arbitrary boundary conditions and may include internal objects which scatter the sound. Some of the equivalent source positions are chosen to be the same as the first order images of the source inside the enclosure, some are positioned within the scattering objects, and the remainder are positioned on a spherical surface some distance outside the enclosure. The normal velocity on the surfaces of the scattering objects and the enclosure walls is evaluated at a larger number of positions than there are equivalent sources. The sum of the squared difference between this velocity and that expected because of the admittance of the boundary, is minimized by adjusting the strengths of the equivalent sources. The convergence of the method is checked by evaluating the velocity at a larger number of monitoring positions. Example results are presented for the sound field and frequency response inside a damped rectangular enclosure, which compare very well with the conventional modal model. The effect of having rigid spheres inside the enclosure are then investigated, and it is found that the effect is significant even some distance from the spheres and at frequencies for which the size of the sphere is small compared to a wavelength. Finally the effect of a nonlocally reacting boundary condition is illustrated by assuming that one of the walls of the enclosure is an elastic plate.