Abstract
Extensive band structures and transmission spectra for 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 have been computed. A periodic pattern of large stop bands is obtained for the airy DSB on a slender water tube. Noteworthy are the interesting results 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.
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