Doppler effects and relativity

[arnesinnema]

I’ve got a question.

Say we have a medium traveling through a pipe at speed v. The soundspeed of the medium is vs. The speed of the wavefronts to an stationary are approximately v-vs and v+vs when both v and vs are much smaller than the lightspeed c. However what happens when v=c? Do the wavefronts move with apparent speed v-vs and v+0 or do they appear to be frozen i.e. v-0 and v+0.

On a similar note, say an electron is traveling around one of the medium atoms in a plane parallel to the direction of movement of the atom. Say the electron is first placed at the front, can it than move backwards? But will stay there? I.e. it cannot move forwards since than the combined speed (relative to the stationary observer) would exceed the speed of light.
I.e. what happens to the Doppler effect at relativistic speeds?

Admittedly I’m not an expert ;).

Regards Arne Sinnema

 

[ProfDawgstein]

However what happens when v=c?

For a medium like water?
Water consists of massive particles (molecules/atoms), which cannot travel at the speed of light.
Nothing massive (m > 0) can reach the speed of light.

If your water goes at $v_{sound}$, your sound wave should "stand still".

For combined speed you might want to check http://en.wikipedia.org/wiki/Velocity-addition_formula#Special_theory_of_relativity.

traveling around one of the medium atoms

That is not easy to answer, you will probably need quantum mechanics for that.