Sound Scattering from Plane Inhomogeneous Surfaces with Acoustic Admittance Changing Periodically along the Surface

A method is given for calculating the scattered sound field from plane inhomogeneous surfaces having normal impedance or admittance independent of the angle of incidence. The expression for the scattered field is represented in the form of power series of a parameter determining the relative inhomogeneity of the surface. A recurrent expression is given for the nth term of the series. Several particular cases are considered in more detail. The proposed method is valid for any ratio λ/L where λ is the wavelength of the incident radiation and L the spatial period of inhomogeneity. A comparison is made with the approximate solution obtained on the assumption that the change of admittance is small at the distance of the order of one wavelength; it means that it is possible to neglect diffraction effects in the immediate vicinity of the surface. A criterion is given for the validity of this approximate method.