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

Abstract

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 performances 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 resultsshow 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 can be expected to yield similar performances when it is used to reproduce

Sound Field Reproduction

“…Other methods have been proposed, whose formulation includes the Kirchhoff-Helmholtz equation and the theory of inverse problems and acoustic holography (see, for example, [Ise99] and [CIB08] [VW04]) and active control of sound [NE92], [EF07]. All the techniques mentioned above have in common the fact that, from the knowledge of a portion of a given sound field, they aim at solving a similar mathematical inverse problem, in order to either reconstruct the acoustic pressure and particle velocity fields near the source (acoustic holography), to identify the sources of sound generating a given field (source reconstruction) or to define the signals driving an array of secondary sources for canceling sound (active noise control) or synthesizing a given sound field (sound field reproduction).…”

Three-Dimensional Sound Field Reproduction Using Multiple Circular Loudspeaker Arrays

“…To determine the spatial placement of the loudspeaker aperture function, we need to find an appropriate radius and elevation angle. Consider (19), in order to calculate β N (kr q ) and Legendre functions properties P N N (cos θ q ) for this circle. From Figure 2, we observe that there are certain elevation angles where the magnitude of the field is quite low or zero.…”

“…We also set β N (k) = 0 for all other circles q = 2 · · · Q, which we will add to the system in the subsequent steps. Thus, (19) reduces to …”

“…A 3D WFS system would thus need an increased number of loudspeakers, which needs to be justified for applied use [18]. In [19], a feasibility study of 3D sound field reproduction at low frequencies was reported by controlling the acoustic pressure measured at the boundary surface of the desired region of reproduction.…”

Experimental validation of sound field control with a circular double-layer array of loudspeakers

“…On the other hand, only a few studies that validate sound field control with loudspeakers experimentally have been published. [10][11][12][13][14][15] These studies have shown that the sound field control is feasible as expected from the simulations, but the exterior region of the loudspeakers array has not been considered.…”