Arrangements of a pair of loudspeakers for sound field control with double-layer arrays

Recent studies have attempted to control sound fields, and also to reduce room reflections with a circular or spherical array of loudspeakers. One of the attempts was to suppress sound waves propagating to the walls outside the array with a circular double-layer array of loudspeakers. The double-layer array represents a set of a monopole and a dipole in the Kirchhoff-Helmholtz integral equation, and thus the distance between these layers should be short compared with the wavelength. In practice, however, this condition is occasionally hard to satisfy because of the sizes of loudspeaker cabinets. In order to solve this problem, this study aims to examine several arrangements of a pair of loudspeakers that has a short distance between the acoustic centres. The effect of diffraction of sound waves due to the enclosure of another loudspeaker is investigated in simulations in terms of the position of the acoustic centre. As a result, it is shown that a loudspeaker has an approximately omni-directional radiation pattern at low frequencies in spite of the other loudspeaker cabinet, but the acoustic centre is shifted to the opposite direction of the cabinets.