An experimental study of end effects for rectangular resonators on narrow channels

Abstract

Quarter-wavelength resonators for harbour entrances and similar applications are usually designed and built without regard to the end effect. This paper describes tests on rectangular resonators using water waves of unique frequency in a long narrow wave channel fitted with a wave generator at one end, a wave absorber at the other end and suitable wave filters. In these tests the wavelength was kept constant while the geometry of the rectangular resonant branch canal was systematically varied. Wave transmission across the resonator, as well as wave reflexion upstream of the resonator was measured. The results clearly indicate a considerable effect of main channel width on optimum resonator width and resonator length, invalidating the usual resonance theory (which predicts complete reflexion of the incident wave train when the length of the branch canal is one-quarter of a wavelength). For example, it is found that, under certain conditions, quarter-wavelength resonators may not have any effect on the incident wave. The work described is limited to the first resonant mode and to semi-infinite domains on each side of the resonator.