Spectral gaps and discrete transmission in slender tubes

Abstract

Extensive band structure and transmission spectra for the longitudinal (acoustic) wave propagation in a system made up of N′ dangling side branches (DSBs) periodically grafted at each of the N equidistant sites on a slender tube are reported. A periodic pattern of large stop bands is obtained for the airy DSB on a slender tube. The emphasis is laid on the interesting result of huge gaps and discrete transmission spectrum due only to the DSB grafted at a single site (N=1) on the slender tube. Designing the system with open tubes allows achievement of lowest gap below a threshold frequency and extending up to zero—thereby providing an entirely discrete band structure and transmission spectrum. This should have important consequences for the suppression of low-frequency noise and for designing filters and transducers.