The reflection of normal modes from a semi-infinite system of barriers in a waveguide

The steady reflection of acoustic waves from a semi-infinite system of equally spaced barriers in a waveguide is investigated. Each barrier consists of a rigid diaphragm with an aperture, which is covered with a rigid moving valve. The valve is coupled elastically to the diaphragm and is capable of performing small oscillations. An exact analytical solution is obtained for the case of a waveguide of arbitrary cross-section, and results of a numerical investigation of the reflection coefficients of normal modes as a function of the frequency of the incident field are presented for the case of the plane problem. For comparison, analytical expressions and graphs of the frequency dependences for the reflection and transmission coefficients of normal modes through one and two similar barriers in the waveguide are given.