Limits of slow sound propagation and transparency in lossy, locally resonant periodic structures

Abstract

We investigate the sound propagation in an air-filled tube periodically\nloaded with Helmholtz resonators. By tuning the Helmholtz with the Bragg\nresonance, we study the efficiency of slow sound propagation in the presence of\nthe intrinsic viscothermal losses of the system. While in the lossless case the\noverlapping of the resonances results in slow sound induced transparency of a\nnarrow frequency band surrounded by a strong and broadband gap, the inclusion\nof the unavoidable losses imposes limits to the slowdown factor and the maximum\ntransmission. Experiments, theory and finite element simulations have been used\nfor the characterization of acoustic wave propagation. Experiments, in good\nagreement with the lossy theory, reveal the possibility of slowing sound at low\nfrequencies by 20 times. A trade-off among the relevant parameters (delay time,\nmaximum transmission, bandwidth) as a function of the tuning between Bragg and\nHelmholtz resonance frequency is also presented.\n