Role of impedance coupling in achieving global active attenuation of noise

Active attenuation of acoustic noise has often been explained using the principle of superposition where a wave from the noise source is added to an out-of-phase wave from the active source. However, the idea of superposition does not increased by the addition of the active source. The expression for the total radiated power is derived and it is shown that the total power can be reduced only when the sources are acoustically coupled. Coupling of the sources' radiation impedances occurs when the sources are connected by a waveguide or are separated by less than one-third of a wavelength in a reflection-free space. The radiation efficiency of the noise and active sources together is controllable via the relative magnitude and phase of the active source when the sources are coupled. For the case where the sources are uncoupled, the nodal positions in the field between the sources and the directivity of the sources are controllable but the total radiated power in the field increases from the addition of the active control source. Impedance coupling between sources is the physical basis for global active attenuation of acoustic noise.