Sonic bands, bandgaps, and defect states in layered structures—Theory and experiment

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Abstract
The propagation of sound through a one-dimensional periodic array of water and perspex plates is studied theoretically and experimentally. It is shown that the passbands and stop bands of a scatterer with a finite number of layers correspond to the bands and bandgaps of an infinite ‘‘sonic bandgap crystal.’’ The transmission coefficient of various finite structures is computed and measured as a function of frequency. The analogy with the electronic bandstructure of crystals, and the photonic bandstructure of macroscopic periodic dielectric structures, is found to be a close one. It is shown that the position and width of passbands can easily be engineered. Results are included for a finite ‘‘crystal’’ with a vacancy defect, in which a narrow passband appears in each of the stop bands.