The transmission loss of a wall incorporating an array of resonators

Resonators, and in particular Helmholtz resonators, are often used to enhance the reflection loss of a given surface. In this paper, the associated effect on transmission loss is analyzed. The mathematical model consists of a rigid moveable wall of infinite extent and molded to form slotted cavities which create an array of line resonators. The pressure within each cavity is governed by the wave equation and the wall motion is assumed to be proportional to the net pressure on the wall surfaces. In response to a normally incident plane wave, the transmitted pressure is determined and numerical results are presented for various configurations. It is shown that the resonator array can significantly enhance the transmission loss of the wall. The effects of slot width, wall mass and the cascading of cavities of differing dimensions are discussed.