Sound Attenuation by a Two-Dimensional Array of Rigid Cylinders

TLDR

The study aims to experimentally analyze acoustic transmission through a two‑dimensional periodic array of rigid cylinders in air, comparing square and triangular lattice configurations. Experimental measurements of sound transmission along the two high‑symmetry directions of the Brillouin zone were performed to assess attenuation characteristics. The results show overlapping attenuation peaks in both lattices above a critical filling fraction, signaling a full acoustic gap, while band‑structure calculations reveal that the triangular lattice contains deaf bands that are not excited in transmission experiments.

Abstract

In this Letter we present an experimental analysis of the acoustic transmission of a two-dimensional periodic array of rigid cylinders in air with two different geometrical configurations: square and triangular. In both configurations, and above a certain filling fraction, we observe an overlap, in the range of the audible frequencies, between the attenuation peaks measured along the two high-symmetry directions of the Brillouin zone. This effect is considered as the fingerprint of the existence of a full acoustic gap. Nevertheless, the comparison with our calculation of band structures shows that the triangular lattice has band states in that frequency range. We call them deaf bands. This contradictory result is explained by looking at the symmetry of the deaf bands; they cannot be excited by experiments of sound transmission.