Calculations on the Sound Reflection from Periodically Uneven Surfaces of Arbitrary Profile

An approximate solution is worked out for the problem of sound reflection when a plane wave is obliquely incident upon an absorbing periodically uneven surface of arbitrary profile.

The groove of the wall is divided into several rectangular regions to obtain an approximate solution. A simultaneous infinite system of linear equations is derived according to the number of the rectangular regions. The equation with the field amplitudes is solved by replacing the system by a finite system. From the solutions, the total reflection factor and the reflecting transfer function at a space point are obtained. In particular, it is found that the reflection factor for an oblique rib array on an absorbing material depends greatly upon the angles of wave incidence (,Φ) in the higher frequency range.