Acoustic phased arrays are capable of steering and focusing a beam of sound via selective coordination of the spatial distribution of phase angles between multiple sound emitters. Here, we propose a controllable acoustic phased array with space-time modulation that breaks time-reversal symmetry, and enables phononic transition in both momentum and energy spaces. By leveraging the dynamic phase modulation, the proposed linear phased array is no longer bound by the reciprocity principle, and supports asymmetric transmission and reception patterns that can be tuned independently. Through theoretical and numerical investigations, we develop and verify a mathematical framework to characterize the nonreciprocal phenomena, and analyze the frequency conversion between the wave fields. The space-time acoustic phased array facilitates unprecedented control over sound waves in a variety of applications including underwater telecommunication.

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