Transmission of Sound through a Circular Membrane in a Plane Wall

The acoustic system studied is that of a plane, rigid wall having a circular window in it, across which is stretched a membrane under tension, in contact with an acoustic medium on both sides. A plane wave of frequency ω/2π is directed at one side of the wall plus membrane, at an angle of incidence θ. The integral equations relating the motion of the membrane and the pressure difference across the membrane are obtained. Fairly accurate solutions to these two equations are then obtained by a variational procedure. Values of the functions involved are plotted and tabulated. Formulas are derived for the total power transmitted through the membrane and for the distribution in angle of the transmitted wave; typical plots are given of the results. These are discussed to demonstrate the contribution of the membrane resonances and anti‐resonances to the transmitted wave. It is known that an unbounded membrane is transparent to an incident plane wave when the wavenumber of the transverse wave in the membrane is eq...