Theoretical and experimental study of transient sound field reconstruction in semi-free field

Abstract

The interpolated time-domain equivalent source method (ITDESM) is based on the assumption of a free field, which might not be suitable for the direct application to a semi-free field. Here, an extended ITDESM procedure is proposed to reconstruct the semi-free transient sound field directly 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. It is assumed 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 the symmetry plane being the reflecting surface. The acoustic contribution from each virtual equivalent source is further formulated with the strengths of the corresponding actual equivalent source to save the computational cost. Reconstruction of the semi-free transient sound fields from three monopoles is contrastively studied by numerical simulations to demonstrate the superiority of the proposed method. This method is also examined by adding noise and measurement point offsets into the reconstruction process, respectively. An experiment with a loudspeaker is conducted in a semi-anechoic chamber, and the results show the validity and applicability of the proposed method.