Estimating the velocity profile and acoustical quantities of a harmonically vibrating membrane from on-axis pressure data (original) (raw)

In this paper an analytic method developed in [1, 2] for the calculation of acoustical quantities such as the sound pressure on-axis, far-field, directivity, and the total radiated power is presented. This method is based on the analytical results as developed in the diffraction theory of optical aberrations by Nijboer [3] and Zernike and Nijboer [4], see also [5, 6]. Using this approach, many of the analytic results in Greenspan [7], such as those on the sound pressure on-axis, the total radiated power, and the results in text books [8] on far-field expressions and directivity can be presented and extended in a systematic fashion. This is worked out in [1] for the results on on-axis pressure and far-field expressions for arbitrary velocity distributions on flat piston radiators. The mathematical foundation of these methods related to directivity and the total radiated power is discussed in [2]. An arbitrary velocity distribution can be efficiently developed as a series in Zernike p...