This has nothing to do with my problem. I have no difficulty with velocity addition, I do have difficulty understanding how relativity can allow waves to travel through vacuum at speeds faster (or just different from) c.
But the reason a wave travels is because the previous state of the wave results in the next state of the wave (eg. light travels because the changing electromagnetic field changes the electromagnetic field around it). So for a wave, state A did make happen state B, er... right?
According to relativity, any wave that can travel through vacuum can do so only at c, because since vacuum looks the same for every observer, so should the mechanism allowing the waves to travel (since that takes place in the vacum) and therefore the speed at which the wave travels (I think)...