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Estimating the Velocity Profile and Acoustical Quantities of a Harmonically Vibrating Loudspeaker Membrane from On-Axis Pressure Data

Formulas are presented for acoustical quantities of a harmonically excited resilient, flat, circular loudspeaker in an infinite baffle. These quantities are the sound pressure on-axis, far-field, 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 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 assessment of loudspeakers in the far-field and of the total radiated power from (relatively near-field) on-axis data (generalized Keele scheme).

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