On the application of difference potential theory to active noise control

The application of the theory of difference potentials to the problem of active shielding and noise control is considered. Difference potential theory allows us to obtain the general solution of the problem in a finite-difference formulation. The solution is valid for arbitrary space domains, medium and boundary conditions. It only requires the information on the total sound (both “friendly” and “adverse”) at the perimeter of the domain to be shielded. In contrast to the previous publications, in the current paper the mechanism of active shielding solution based on the difference potential theory is analysed. The theory of difference potentials is applied to the system of acoustic equations. The correspondence between the finite-difference solution and the continuous solution based on Green's function is shown for the case of a uniform medium. Different possible representations of the active shielding source terms are analysed. A clear physical interpretation of the optimal space step in the finite-difference solution is provided. The results can be important for both understanding the solution of the active shielding problem and practical applications.