A pressure field in an acoustic medium containing a cylindrical solid and a sphere oscillating in a predetermined manner

fA problem on the interaction of a spherical body oscillating in a predeter mined fashion and a rigid cylinder is formulated, The bodies do not interse ct, are immersed into an ideal compressible liquid, and their centers are i n one plane. The solution is based on the possibility of representing the p artial solution of the Helmholtz equation, written in cylindrical coordinat es, in terms of partial solutions in spherical coordinates, and vice versa, An infinite System of linear algebraic equations is obtained by satisfying the boundary conditions on the sphere and cylinder surfaces. The system is intended for determining the coefficients of the expansion of the velocity potential into a series in terms of spherical and trigonometric functions. The system obtained is solved by the reduction method. The appropriateness of this method is substantiated. The hydrodynamic characteristics of the l iquid surrounding the spherical and cylindrical bodies are determined. A co mparison is made with the problem on a sphere oscillating in an infinite in compressible liquid that contains also a cylinder and in a compressible liq uid that contains nothing more. Two types of motion of the sphere - pulsati on and oscillation - are considered.