Modeling of ultrasonic waves propagation in the time domain is required for many industrial applications, such as ultrasonic nondestructive testing, ultrasonic flow measurement, biomedical ultrasound, etc. Such applications often imply the computation of wave propagation over distances of hundreds of wavelengths, which makes them challenging for traditional time-implicit finite element schemes. On the other hand, the time-explicit nodal discontinuous Galerkin finite element method has proven to be an efficient tool for solving acoustically large problems in the time domain. This method provides high accuracy, great scalability, and low memory consumption.The ultrasonic wave propagation problems typically involve multiphysics phenomena, such as acoustic-structure interaction and piezoelectricity. Piezoelectric units are used as transmitters and/or receivers of the signal that propagates in coupled acoustic-elastic media. The multiphysics phenomena are incorporated into the proposed numerical approach which is based on solving of the acoustic-structure interaction problems in the form of a coupled acoustic-elastic first-order hyperbolic system. An extra second-order stationary partial differential equation is solved for the electric potential in the piezoelectric domains.