This is quite nuanced and not as most people assume.
It is the "phase velocity of light in that medium" that is exceeded.
phase velocity of light in a medium = speed of light / refractive index of the medium.
Thus the EM wave is slowed down in a medium and so a charged particle can exceed it producing Cherenkov radiation. This is similar to a sonic boom in atmosphere when speed of sound is exceeded. In both cases the object is traveling faster than the wavefront.
It is only in vacuum that "phase velocity of light" = "group velocity of light" = c (i.e. 300,000 km/sec)
What really is the speed of light in a medium/vacuum, group or phase velocity? - https://physics.stackexchange.com/questions/450377/what-real...
IIRC the group velocity in a medium can also exceed c when you send pulses through certain nonlinear media. Basically, the "lump" of the pulse can appear to "exit before it entered," but what really happens is that the tiny tip of the pulse has already gone through at <= c, and starts growing into the body at the exit before it has completely shrank at the entrance because of the nonlinearity. So it is actually the information/"signal" velocity (the tip of the signal) that cannot exceed c.
AFAIK there are three scenarios;
1) Non-Dispersive medium (eg. vacuum) : v(g) = v(p) = c
2) Normal Dispersion medium (eg. in water) : v(g) < v(p)
3) Anomalous Dispersion medium (eg. absorbing materials) : v(g) > v(p)
where (simplified);
v(g) : group velocity which can be thought of as a function of the overall wave packet (i.e. pulse) and hence contains the actual energy/information/signal.
v(p): phase velocity which can be thought of as a function of a single wave frequency and hence the crest of that wave.
Are there interesting relativistic effects related to this other than this Cherenkov radiation?
Yes, there are. Checkout the "see also" section of Cherenkov radiation on wikipedia which lists some of them - https://en.wikipedia.org/wiki/Cherenkov_radiation
Here is the relevant chapter from the Feynman lectures, Relativistic Effects in Radiation - https://www.feynmanlectures.caltech.edu/I_34.html
If you ask AI, you will get a list with nice short explanatory notes; check it out.
Finally on a related and very interesting vein, Physicists have even brought light to a standstill in tiny gas clouds of sodium atoms cooled to near absolute zero! See the pdf of Scientific American article "Frozen Light" by Lene Vestergaard Hau from her publications webpage - https://groups.seas.harvard.edu/haulab/publications/HauPubli...
To be more perfectly precise, it is only in a vacuum with an infinitely repeating regular signal that "phase velocity of light" = "group velocity of light".
The deviation caused by uncertainty in the package arrival time is typically extremely short, but not zero, for finite signals.
The actual "entity" that is restricted to be <=c is "information velocity". An infinitely repeating pattern would have travel at (phase velocity)=c ... but would ironically transmit no actual information (the bit value is restricted to 1, not 0 or 1).
Nice. Trying to read/understand "RF Systems and Modulation" is what got me interested in this subject in the first place.
So in my mind i map your comment as; the "carrier signal" single analog frequency is the infinitely repeating regular wave (no information) traveling at v(p) while the "information signal" (analog/digital) imposed on top of it (frequency/amplitude/phase modulation) creates the informational pulse/wave packet traveling at v(g).
Add in different media in the real world and you have a difference between v(g) and v(p) - https://news.ycombinator.com/item?id=49988070