  We find a new set of exact solutions to Maxwell's equations in space--time
varying materials, where the refractive index is constant, while the impedance
exhibits effective motion, i.e. it is a function of $x-vt$. We find that waves
co--propagating with the modulation are not reflected within the material,
while counter--propagating waves are continually reflected by the changing
impedance. For a finite section of such a material we find analogues of
transmission resonances, where specially shaped `eigenpulses' enter without
reflection. We also find that there is a strong asymmetry in reflection from
the medium when the impedance modulation is small but rapid, the material
reflecting strongly from one side, and negligibly from the other. Unlike
stationary media, the spectrum of the reflected wave can be significantly
different from the incident one.
