Immersive wave control experimentation using compensated directive sources

Abstract

A physical boundary with embedded active sources can cancel acoustic waves incident on the boundary and also synthesize waves to fully control the acoustic field in an experimental setup (e.g., a water tank) such that the physical experiment is artificially immersed into a virtual domain and waves propagate seamlessly between the physical experiment and virtual domain. The acoustic representation theorem at the heart of the immersive experiment requires physical monopole sources to be deployed on the active boundary. However, real physical sources (e.g., piezoelectric transducers) project waves at sonic frequencies (e.g., 2–20 kHz) that do not fully conform to the theoretically required radiation pattern. If left uncorrected, using these physical sources causes the wavefield to deviate from those desired in immersive experiments. A method is proposed to compensate for the non-monopolar radiation pattern of the sources, and the compensation is incorporated into the Kirchhoff-Helmholtz extrapolation, which is used to determine the controlling field at the active boundary in real-time. Numerical simulations show that the method can effectively compensate for the undesired effects caused by such sources. The method is implemented as a pre-processing step that modifies the extrapolation Green's functions in the Kirchhoff-Helmholtz integral before the actual experiments take place and can be physically interpreted in terms of Huygens’ principle.