Acoustic field in a rigid cylindrical vessel under excitation by pulsating sphere (Q2754695)

Solving the problem of harmonic acoustic field is reduced to the solution of Helmholtz equation inside a cylinder. Boundary conditions express zero velocity (normal derivative of wave potential) at the rigid wall of cylinder and a prescribed value of pressure (wave potential) at the surface of a sphere located at the center of cylinder. Solution is sought in the form of two functions satisfying the Helmholtz equation in cylindrical and spherical coordinates respectively. Fulfillment of boundary conditions requires re-expansion of the solutions in another coordinate system. As a result, an infinite algebraic system for coefficients of expansions is derived. Distributions of pressure and velocity are plotted and analyzed. Solution is compared with the field radiated by oscillating sphere in infinite volume.