The band structure of two kinds of phononic crystals (the square lattice of mercury (water) rods in a water (mercury) host) has been calculated using the plane-wave expansion method based on super cell. The translation group symmetry of phononic crystal is changed by changing the size of adjacent rods. We found that by changing the lengths of sides of adjacent rods one can effectively adjust the phononic band gaps. The present work shows that the translation group symmetry of phononic crystal has an important influence on the formation of its band gaps, and the method based on super cell is an effective method of studying the influence of translation group symmetry of phononic crystal on the formation of phononic band gaps.
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