Tangential Impedance

The problem of reflection of a plane sound wave from a rigid surface covered with dipole resonators is solved. It is shown that such a surface responds to obliquely incident waves, while the found angular dependence of the reflection coefficient cannot be obtained for surfaces whose properties are described by conventional impedance. Therefore, the concept of tangential impedance is proposed: the ratio of tangential acoustic force on a surface to its normal velocity. It is shown that the tangential impedance can be both isotropic and anisotropic; i.e., the magnitude of the latter depends on the direction of the incident wave. It is proposed to call the corresponding surfaces unpolarized and polarized. In some cases, tangential impedance can be useful for macroscopic description of complex metasurfaces.