Minimization of acoustic power in free space using multiple distributed sound sources (On the generation condition of the zero control power phenomena)

Abstract

Low-frequency noise is difficult to suppress by passive control using a sound absorbing material. Active noise control is expected to be an effective method against low-frequency noise. Minimizing the total acoustic power emitted by a sound source causes a zero control power phenomena. In the zero control power phenomena, the absorption and blowout of sound energy around the control source are balanced, and the time average of the control power becomes zero. Therefore, control power suppression may be able to minimize total sound power. Previous studies have assumed that the sound source is a monopole sound source or a piston embedded in an infinite baffle, so there are restrictions on the sound source. In this research, we aim to generalize the zero control power phenomena the sound sources are regarded as flat plate structures embedded in an infinite baffle, and the conditions under which the zero control power phenomena occurs are examined. We clarify the occurrence conditions for zero power phenomenon when one noise source and n control sound sources are used. The specific conditions for the zero control power phenomena in multiple sound sources which are the newly defined in this paper inter source mobility reciprocity are established between the noise source and each control sound sources. In addition, numerical calculations are performed based on the derived control law to clarify the effect of the number of control sound sources and the sound sources position on the acoustic power. In addition, the relationship between the wavelength and the suppression effect is examined from a numerical point of view.

Keywords

• active noise control
• zero control power phenomena
• acoustic power
• total sound power minimization
• circulant matrix