Comparison of spheroidal and eigenfunction-expansion trial functions for a membrane in an infinite baffle

The on-axis far-field pressure response of a circular membrane in an infinite baffle when driven by a uniformly distributed electrostatic force is calculated using two different trial functions for the surface velocity distribution. The first is an expansion based upon a solution to the free space wave equation in oblate spheroidal coordinates, which has already been derived in a previous paper J. Acoust. Soc. Am. 120(5), 2460-2477 (2006)], and the second is a membrane eigenfunction expansion (or Bessel series), which is rigorously derived in this letter. Although the latter can be used as a basis for calculating a number of different radiation characteristics such as the radiation impedance or directivity, etc., only the on-axis far-field sound pressure is considered here. The results are compared and discussed.