  Nowadays, there is considerable interest in metamaterials which realize the
electromagnetically induced transparency in a classical system. We consider the
frequency shifts of particle moving in metamaterials exhibiting
electromagnetically induced transparency effect. The dramatic change of the
material dispersion due to the EIT influences the conditions for signal
propagation in the medium and has a significant impact on the Doppler effect,
possibly leading to the optical control over this phenomenon. The dependence of
the Doppler shift to the source frequency and velocity and radiation spectra on
external parameters is examined. It was found that for source frequencies
fitting transparency window for particular range of source velocities cutoffs
appear, i.e. the radiation is not emitted. Our theoretical findings are proved
analytically and confirmed by numerical simulations based on finite-difference
time-domain method.
