If a tachyon starts from where you are and goes away at faster than the speed of light, you will see the photons it emits earlier than it actually departs.
So you will see all these photons coming as if the tachyon were coming toward you at a speed slower than light, and then bang, the tachyon leaves.
In fact, the faster it is going away, the slower it appears to be arriving.
EDIT: You can just tell this from a space-time diagram:
T s C
| / /
|/ / f
| s / /
|/ / f /
| / / /
|/__/_/___X
| / /
| / /
|/ /
| /
|/
Here, the time T axis is vertical and the space X axis is horizontal.
Line C represents the speed of light. Photons move parallel to that line.
If something is moving away from you slower than light, it is a diagonal line falling in the slow (s) region. When it emits photons, they travel parallel to C, so each one arrives back at you at a later time.
That's the normal behavior that you're used to.
If something is moving away from you faster than light, it is a diagonal line in the fast (f) region. When it emits photons, they travel parallel to C, and thus arrive back to you at a negative time, relative to when the object left you.
In fact the faster it's moving (closer to horizontal) the earlier its photons will arrive (negative T).
The slower it's moving (closer to C) the more its photons will appear to come all at once, just before it "departs".
Best Answer
Speed of sound in air is the speed with which a pressure wave propagates. If you look at the wave itself, without considering its source, you have all the information you need to determine the speed of propagation - since it's only the local conditions (things like the density, and the local rate of change of pressure) that determine this.
The same is true with light: if you "look at a photon passing you", you don't need to know anything about the source - once the signal (sound or light) has left its source, it loses all memory of that, and just becomes a wave that propagates.
Now the laws of addition of velocities that we use in relativity are related to the postulate that the speed of light will be the same in any inertial frame of reference; the Lorentz transformation follows directly. But there is no equivalent claim for sound. The fact that supersonic travel exists pretty much proves that. One a more basic level, if you are standing downwind from a sound source, that sound will reach you more quickly than if you were standing the same distance upwind - because the pressure disturbance travels with the bulk of the medium.
It follows that the speed of sound depends on the observer's velocity relative to the medium.