Active control of noise radiated from a long cylinder: Can the Nyquist limitation be broken?

In the present paper, we consider active control of noise propagating from a long cylinder. For that purpose control sources are distributed on the external surface of the cylinder. They provide a secondary sound field which enables them to compensate for the noise field propagating outside. To implement active noise control, we apply an approach based on the Calderón potentials that have the projection property. Numerical simulations to attenuate broadband noise with different numbers of control sources per wavelength are carried out. The effect of the cylinder on the Green's function and consequent noise attenuation is studied. There are two key findings in this paper. First, the results demonstrate that the level of relative noise attenuation remarkably increases along with the growth of the distance. Second, it is shown that even less than two control sources per wavelength can provide essential noise cancelation. At first glance, this result contradicts the well-known Nyquist-Shannon sampling theorem. A theoretical explanation of this result is provided.