Eigenoscillations of an acoustic cavity with a local membrane

Abstract

On the basis of Strutt’s approach, the problem of eigenoscillations of a gas in a cylindrical cavity with an internal membrane in the presence of a coaxial circular aperture in it (A.N. Fock’s problem) is analyzed. By an adequate numerical−analytical procedure, a high-precision solution is constructed to a boundary value problem for the eigenfrequencies and forms of lower order oscillation modes for various relative values of the aperture radius. A (qualitative and quantitative) correspondence is established to the results known in acoustics as applied to the concept of the “associated mass of an aperture.” New physical effects are obtained on the dependence of the frequencies and forms of long-wavelength oscillations of a gas on the geometric parameters of the system.