On the sound field of a resilient elliptical disk in an infinite baffle

A resilient elliptical disk has zero mass and stiffness and is driven by a uniform pressure distribution rather than uniform velocity as would be the case for a rigid disk. It can represent the diffraction of a plane wave through an elliptical aperture in an infinite rigid screen of zero thickness as well as provide an idealized model of a loudspeaker of the electrostatic or planar magnetic type. Using the Fourier (Hankel) Green's function in cylindrical coordinates, together with the monopole Kirchhoff–Helmholtz boundary integral, rigorous analytical formulas are derived for calculating the surface velocity distribution, radiation admittance, on-axis pressure, and directivity pattern of an elliptical resilient disk in an infinite baffle and these are plotted over a range of normalized frequencies. The directivity is compared with that of a resilient circular disk and asymptotic low-frequency approximations are derived for the radiation resistance, reactance, and on-axis pressure.