We find a set of exact solutions to Maxwell's equations in spacetime-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 copropagating with the modulation are not reflected within the material, while counterpropagating waves are continually reflected by the changing impedance. For a finite section of such a material, we find analogs 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. Published by the American Physical Society 2024