On some approach to active noise control

The problem of active shielding and noise control is considered. In this problem one domain is shielded from the noise generated in another domain via an implementation of additional sound sources situated outside of the first domain. The general solution of the problem in a finite-difference formulation can be obtained using the difference potential method. This solution appears to be valid for arbitrary domains, medium and boundary conditions. It only requires the information on total sound (both desirable and undesirable) at the perimeter of the domain to be shielded. Currently all analysis and applications of the difference potential solution have been limited by the Helmholtz equation. In contrast to the previous publications, in the current paper the mechanism of the active shielding solution is analysed. For this purpose, the case of monochromatic wave propagation in a duct with an end termination is studied. The difference potential method is first applied to the system of acoustics equations. The correspondence between the finite-difference solution and continuous solution based on the Green function is shown for the case of a uniform medium. Different possible representations of the active shielding terms are analysed