Abstract
The behavior of an acoustic wave in a periodic lattice was mathematically shown for both infinite and finite cases. For simplicity, the lattice is assumed to be composed of two kinds of medium in ABABABAB order for the infinite case, and BBBABABABABBB order for the finite case. For the infinite lattice, by using the Blochs theorem, the dispersion relation of the wave in the periodic lattice was driven. This gives an acoustic band gap (the frequency region that the wave cannot propagate) and negative group velocity. In addition, for the finite lattice, by using symmetry and the superposition principle, reflection coefficient (between the outer medium and the lattice surface) and transmission coefficient (through the finite lattice) were driven. It was then shown that the result of the finite case agrees to the result from the infinite lattice case, if the number of periods goes to infinity. Finally, possible applications by using what we have learned would be discussed.
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