In this paper, we investigate the propagation of electromagnetic waves in a piezoelectric composite comprising carbon nanotubes and piezoelectric fibers. This hybrid medium is initially subjected to the effects of an extremely short optical pulse consisting of just two oscillations of the electric field. On the basis of Maxwell's equations and the wave equation for the displacement vector of the medium, we obtain an effective governing equation for the vector potential of the electromagnetic field, as well as the displacement vector for the media. The dependence of the pulse shape on the parameters of the problem was analyzed, thereby revealing a non-trivial interplay between the characteristics of the pulse dynamics and the electrically induced mechanical vibrations of the medium. The uncovered properties could potentially offer promising prospects for the development of new materials for the optoelectronics industry.