Estimating the velocity profile and acoustical quantities of a harmonically vibrating loudspeaker membrane from on-axis pressure data

Formulas are presented for the acoustical quantities of a harmonically excited resilient, flat circular loudspeaker in an infinite baffle, which are the sound pressure both on axis and far field, the directivity, and the total radiated power. These quantities are obtained by expanding the velocity distribution in terms of orthogonal polynomials. For rigid and non rigid radiators this yields explicit series expressions for both the on-axis and the far-field pressure. In the reverse direction, a method of estimating velocity distributions from (measured) on-axis pressures by matching in terms of expansion coefficients is described. Together with the forward far-field computation scheme, this yields a method for the assessment of loudspeakers in the far field and of the total radiated power from (relatively near-field) on-axis data (generalized Keele scheme).