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The geometric-phase concept has far-reaching implications in many branches of physics^{,,,,,,,,,,,,,}. The geometric phase that specifically characterizes the topological property of bulk bands in one-dimensional periodic systems is known as the Zak phase^,. Recently, it has been found that topological notions can also characterize the topological phase of mechanical isostatic lattices. Here, we present a theoretical framework and two experimental methods to determine the Zak phase in a periodic acoustic system. We constructed a phononic crystal with a topological transition point in the acoustic band structure where the band inverts and the Zak phase in the bulk band changes following a shift in system parameters. As a consequence, the topological characteristics of the bandgap change and interface states form at the boundary separating two phononic crystals having different bandgap topological characteristics …