  We investigate elastic wave propagation in finitely deformed dielectric
elastomers in the presence of an electrostatic field. To analyze the
propagation of both longitudinal (P-) and transverse (S-) waves, we utilize
compressible material models. We derive explicit expressions of the generalized
acoustic tensor and phase velocities of elastic waves for the ideal and
enriched dielectric elastomer models. We analyze the slowness curves of the
elastic wave propagation, and find the P-S-mode disentangling phenomenon. In
particular, P- and S- waves are separated by the application of an electric
field. The divergence angle between P- and S-waves strongly depends on the
applied electrostatic excitation. The influence of the electric field is
sensitive to material models. Thus, for ideal dielectric model the in-plane
shear velocity increases with an increase in electric field, while for the
enriched model the velocity may decreases depending on material constants.
Similarly, the divergence angle gradually increases with an increase in
electric field, while for the enriched model, the angle may be bounded.
Material compressibility affects the P-wave velocity, and, for relatively
compressible materials, the slowness curves evolve from circular to elliptical
shapes manifesting in an increase of the reflection angle of P-waves. As a
results, the divergence angle decreases with an increase in material
compressibility.
