  Analyzing paradoxes is interesting and instructive. Sometimes the analysis
leads to non-trivial results. This methodological note sets out a paradox
arising in the theory of propagation of electromagnetic waves in moving
plasmas. The paradox is interesting in itself, and, generally speaking, it
should be taken into account when analyzing geoelectromagnetic waves. The
paradox is as follows: contrary to expectations, the group velocity of the
waves is the same in the comoving and laboratory frames of reference. The
condition for the appearance of the paradox is the quadratic dependence of the
frequency on the wave number. A paradoxical property manifests itself in the
theory of the propagation of radio waves (in particular, whistling
atmospherics), Langmuir waves and Alfv\'en waves. From a cognitive point of
view, it is interesting that the paradox can be traced in relation to de
Broglie waves. An explanation of the paradox is proposed. Keywords: group
velocity, moving plasma, Doppler Effect, dispersion, longitudinal waves,
transverse waves.
