An improved scattering matrix method is developed to study a two-dimensional air-rigid sonic crystal with open resonant cavity, and the band structure and transmission properties are investigated. Numerical results show that both the band structure and the transmission coefficient are sensitive to the shape of the resonant cavity. The relationship between the resonant band gap and the shape of the resonant cavity is given. The high effective refractive index and the transmission ratio in the long wave range make such a system a good material for a sound lens.
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Hou et al. (2007) studied this question.
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