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On the sound field of a resilient elliptical disk in an infinite baffle
1Mellow Acoustics Ltd, 42 Hale Road Farnham, Surrey GU9 9QH United Kingdom.
Abstract:
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.
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