The acoustic field in a rigid cylindrical vessel excited by a sphere oscillating by a definite law

The problem on the interaction between a spherical body oscillating by a de finite law and a rigid cylinder filled with an ideal compressible liquid is formulated. The geometrical center of the sphere is located on the cylinde r axis. The solution is based on the possibility of representing the partic ular solutions of the Helmholtz equation in cylindrical coordinates in term s of particular solutions in spherical coordinates, and vice versa, As a re sult of satisfaction of the boundary conditions on the surfaces of the sphe re and cylinder, an infinite system of linear algebraic equations is obtain ed to determine the coefficients of expansion of the potential of liquid ve locities into a Fourier series in terms of Legendre polynomials, The use of the reduction technique for solving the infinite system obtained is substa ntiated. The hydrodynamic characteristics of the liquid filling the cylindr ical cavity are determined and compared with the case of a sphere vibrating in an infinite liquid.