Gravitational and acoustic waves due to the motion of an oscillating thin plate beneath the surface of a heavy weakly-compressible fluid

The three-dimensional problem of the motion of a thin plate in an inviscid, heavy, weakly-compressible fluid is solved. The surface tension is disregarded. The plate moves rectilinearly at a constant velocity under the surface of an infinite-depth fluid and oscillates at a given frequency. The fluctuating dipole potential is obtained from the Euler and continuity equations with account for the conditions on the free surface (linear theory of small waves) and the conditions at infinity. The density distribution function of the dipole layer is determined from the boundary conditions imposed on the plate surface. Formulas for calculating the far acoustic field are derived. The calculations for a square plate are carried out.