Reconstruction of Semi-free Transient Sound Field Based on an Extended Interpolated Time-domain Equivalent Source Method

Interpolated time-domain equivalent source method (ITDESM) is based on the assumption of free field, which might not be suitable for the direct application to the semi-free field. Here, an extended ITDESM procedure is proposed to reconstruct the semi-free transient sound field in the time domain. In this method, the time-domain equivalent sources are placed not only near the actual sound source, but also near its image source. Assume that the number of the equivalent sources distributed around the image source (virtual equivalent sources) is identical to that distributed around the actual source (actual equivalent sources), and their locations are mirror-symmetric with symmetry plane of the reflecting surface. According to the image theory, the acoustic contribution from each virtual equivalent source is further formulated with the strengths of the corresponding actual equivalent source. Hence, the computational cost of solving the equivalent source strengths is reduced by nearly half. Reconstruction of the semi-free transient sound fields from three monopoles is contrastively studied by numerical simulations to demonstrate the superiority of the extended ITDESM. An experiment with a loudspeaker is conducted in a semi-anechoic chamber, and the results show the validity and applicability of the proposed method.

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