The oscillations of a compressible fluid within a region bounded by a flat plate on one side and an acoustically soft boundary on the other are studied. A supersymmetric structure of the resolvent is established. It is shown that, because of the presence of the supersymmetry, the solution has properties in common with the solution to the quantum-mechanical problem of an electron in a magnetic field. The connection between supersymmetry and the symmetry group of the problem is demonstrated.