Acoustic phonons can be coherently generated by ultrafast displacive screening of potential gradients, often enhanced by the strong built-in piezoelectric fields, in wurtzite semiconductors. In such structures, transverse symmetry within the c plane hinders both the generation and detection of the transverse acoustic (TA) modes, and only longitudinal acoustic (LA) mode is generated. We show that even for c-GaN, the application of asymmetric potential distributions in the c plane can break the symmetry and selection rules, thus switching on the normally forbidden TA mode. This is in contrast to the LA mode, the strength of which varies with the symmetric potential distributions. By comparing transient differential reflectivity spectra in structures with and without asymmetric potential distributions, the role of the electrically attained anisotropy was further revealed by the digitized appearance of the TA mode, in clear contrast to the monotonic LA mode, and by modulations in the propagation velocities, optical birefringence, and geometrically varying sensitivities, the underlying mechanisms of which are modeled by electric-field-dependent perturbations of the dielectric tensors, incorporating the results of elastic modulations.