Analysis of frequency band structure in one-dimensional sonic crystal using Webster horn equation

Abstract

Sound propagation through periodic arrangement of scatterers lead to formation of bands of frequencies, known as band gaps, where sound cannot propagate though the structure. We propose a method based on Webster horn equation, along with Floquet theorem, to predict the band gap of a one-dimensional periodic structure made of hard sound-scatterers. The method is further modified to obtain the complex wave numbers, which give the decay constants. The decay constant is used to predict the sound attenuation of the evanescent wave in the finite sonic crystal. The theoretical prediction is verified with experimental measurements.