Soft dielectric tubes undergo large deformations when subjected to radial voltage. Using the theory of nonlinear electroelasticity, we investigate how voltage-controlled deformations of these tubes in an array alter acoustic wave propagation through it. We show that the propagation is annihilated across a certain audible frequency range, referred to as a sonic band gap. We carry out a numerical study, to find that the band gap depends nonlinearly on the voltage, owing to geometrical and material nonlinearities. By analyzing different mechanical constraints, we demonstrate that snap-through instabilities resulting from these nonlinearities can be harnessed to achieve sharp transitions in the gap width. Our conclusions hint at a new strategy to adaptively filter sound using a simple control parameter - an applied voltage.