Transmission and Trapping of Waves in an Acoustic Waveguide with Perforated Cross-Walls

Abstract: Trapping and transmission of waves through an acoustic waveguide with a set of perforated cross-walls are studied. Eigenvalues of the corresponding spectral Neumann problem for the Laplace operator are found under geometric symmetry conditions. Almost complete transmission of the piston wave through a system of small holes (an inverted Weinstein anomaly) is achieved by fine tuning of the distance between the cross-walls with a diverse configuration of the connecting holes. A criterion for the possibility of this anomaly is obtained. Related topics—in particular, primitive wave filters and the pinhole-camera effect—are discussed.