Spherically symmetric acoustic propagation across a fluid/fluid boundary

Abstract

The problem of determining the spherically symmetrical field generated by an acoustic point source at the center of a fluid sphere that itself is immersed in a second fluid medium is discussed. A method of solving for the field in the internal and external fluid regions is introduced, based on finite Hankel transforms. These transforms and their inverses are constructed in such a way that the boundary conditions (continuity of pressure and normal component of particle velocity) at the spherical interface are satisfied. In particular, the inverse transforms are integrals; that is, there is a continuum of radial wavenumbers. This contrasts with the more usual formalism, involving a Fourier–Bessel series taken over a discrete distribution of radial wavenumbers. The latter type of inversion formula is suitable only for problems involving relatively simple boundary conditions (e.g., Dirichlet or Neumann). Using the new technique, an exact analytical solution is given for the acoustic field in both the sphere and the surrounding fluid.