A method for reconstruction of boundary conditions of an arbitrarily shaped three dimensional sound source from a finite number of significant figure of field pressures is presented and the associated sound field is predicted by using the Helmholtz integral equation.
To minimize the reconstruction error due to noise in the field pressures, a filtering method is proposed and it is verified that numerically singular values which correspond to the higher-order modes of the evanescent-like components of the source velocities are eliminated. For arbitrarily shaped sources with complex boundary conditions, source reconstruction is performed accurately when the size of each element is about a quarter wavelength and the field measurement positions are equally or randomly distributed on the surface of sphere in the vicinity of the source. High performance is obtained for a measurement surface which is very closed to the sound source since the rapidly decaying evanescent-like components of the source velocities can be detected much.
The reconstruction error of higher order evanescent-like components does not affect the reprediction of its associated field. Therefore, it is desirable to estimate the reconstruction efficiency on the basis of the accuracies of the repredicted near field pressures and acoustic power in cases when one reconstructs the source boundary conditions in order to repredict the total sound field.
Our technique can be used in computer-aided loudspeaker design that reconstructs loudspeaker diaphragm velocities from finite number of measured field pressures and repredicts the variation of the sound field produced by redesigned loudspeaker cabinets on which the reconstructed diaphragm are mounted.
The method thus provides a new way in which acoustic measurement can be used to determine vibration patterns, and consequently further possibilities for non-contacting investigation of the velocities of sound source such as loudspeaker diaphragm.