Compensating for source directivity in immersive wave experimentation

A physical boundary mounted with active sources can cancel acoustic waves arriving at the boundary, and emit synthesized waves into the neighboring medium to fully control the acoustic wavefield in an experimental setup such as a water tank or air-filled cavity. Using the same principles, a physical experiment can be artificially immersed within an extended virtual (numerical) domain so that waves propagate seamlessly between the experimental setup and virtual domain. Such an immersive wave control experiment requires physical monopolar sources on the active boundary. However, real physical sources (e.g., piezoelectric transducers) project waves at middle-to-high sonic frequencies (e.g., 1–20 kHz) that do not fully conform to the theoretically required monopolar radiation pattern; if left uncorrected, this causes controlled wavefields to deviate from those desired in immersive experiments. A method is proposed to compensate for the non-monopole-like radiation patterns of the sources, and can be interpreted physically in terms of Huygens principle. The method is implemented as a pre-computation procedure that modifies the extrapolation Green's functions in the Kirchhoff-Helmholtz integral before the actual experiments take place. Two-dimensional finite-difference simulations show that the processing method can effectively suppress the undesired effect caused by non-monopolar active sources in immersive wave control experiments.