Topological interface states and the associated enhancement of sound intensity in periodic systems is of fundamental interest in wave physics and may have wide applications, such as in sound detection and biomedical imaging. Yet their occurrence is hitherto limited to the topological transition where the bands inverse. Here we theoretically design and experimentally demonstrate an 'acoustic heterostructure'capable of giving rise to interface states at arbitrary frequency within the topological band gap, which is accomplished by adjusting a single structural parameter. The remarkable sound-intensity enhancement, which reaches 104, is not affected by this change but remains near constant within the said frequency range and is tested in both a sonic and an elastic wave setting. We envision our strategy to be useful in the design of alternative acoustic sensors and detectors with high flexibility and sensitivity in diverse scenarios, such as nondestructive detection and medical imaging.