Acoustic spectral gaps and discrete transmission in slender tubes

Abstract

This work reports on the band structure and transmission spectrum for the longitudinal (acoustic) wave propagation in a system made up of N′ dangling side branches (DSB) periodically grafted at each of the N equidistant sites on a slender tube. A periodic pattern of large stop bands is obtained for the airy DSB on the slender water 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 the 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.