Acoustic spectral gaps and discrete transmission in slender tubes

We report 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 a slender water tube. We emphasize the interesting result of huge gaps and the 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. (C) 1998 Published by Elsevier Science Ltd.