Effects of periodically corrugated surfaces on sound scattering

Periodic structures have been used in soundscape design to achieve noise control while maintaining aesthetic purposes. As a kind of periodic structure, periodically corrugated surfaces can work as spatial frequency-selective filters to generate marvelous acoustical phenomena. This paper investigates the effects of periodically corrugated surfaces on sound scattering with an analytical method based on the Kirchhoff-Helmholtz equation and proposes a perturbation method to give an approximate solution to the scattered sound pressure with much less computation time. Three different kinds of corrugated surfaces with periodic right triangle, isosceles triangle and sinusoidal steps are considered. It is found that the fundamental frequency of scattered sound is mainly determined by the period of the surface while the relative amplitude of the harmonics to the fundamental frequency is affected by the step height. Experiments with 3D printed scale models in the anechoic chamber support the simulation results. Measurements in Mount Maoshan demonstrate that sound scattered from right triangle steps sounds like trumpet solos with the fundamental frequency and all the harmonics of almost the same amplitude. Scattered sound of different timbres can be designed with periodic surfaces of different shapes, which might have potential applications in soundscape design.