On the sound field of a circular membrane in free space and an infinite baffle

Abstract

An enhanced method for calculating the radiation characteristics of a tensioned circular membrane in free space is presented using an analytical solution to the infinite integral in the free-space Green’s function in cylindrical coordinates. This enables direct calculation of the surface pressure series coefficients by equating the coefficients of the resulting Bessel series in a set of simultaneous equations. Eliminating both numerical integration and least-squares minimization improves calculation speed and accuracy. An infinite baffle is introduced to provide an indication of what the theoretical limit of the bass performance would be using a very large enclosure. Furthermore, analytical solutions to the pressure field integrals are presented. A force transmission coefficient is introduced, which is the ratio of the total radiation impedance to the motional impedance. The motional, radiation, and diaphragm impedances of the damped membrane are calculated, together with the near- and far-field pressure responses and efficiency. A comparison is made between the on-axis response (without damping) calculated using this method and using a finite element model. It is demonstrated that good correlation between the two calculation methods can be achieved provided the elements are small enough and a sufficiently large model is used at the frequency extremes.