Active control of sound inside a sphere via control of the acoustic pressure at the boundary surface

Here we investigate the practical feasibility of performing soundfield reproduction throughout a three-dimensional area by controlling the acoustic pressure measured at the boundary surface of the volume in question. The main aim is to obtain quantitative data showing what upper frequency limit a practical implementation of this strategy is likely to yield. In particular, the influence of two main limitations is studied, namely the spatial aliasing and the resonance problems occurring at the eigenfrequencies associated with the internal Dirichlet problem. The strategy studied is first approached by performing numerical simulations, and then in experiments involving active noise cancellation inside a sphere in an anechoic environment. The results show that noise can be efficiently cancelled everywhere inside the sphere in a wide frequency range, in the case of both pure tones and broadband noise, including cases where the wavelength is similar to the diameter of the sphere. Excellent agreement was observed between the results of the simulations and the measurements. This method could be used to reproduce low-frequency soundfields, in which case similar performances are expected to be yielded.