Some extended analyses concerning the physics and kinematics of wave propagation in moving systems:

http://www.springerlink.com/content/7qhkh06643838577/ Waves from a moving source does not propagate with equal velocity in each direction:

c '= c (1 - e ^ 2) / (1 + e cos (phi));

c - the nominal speed of waves, eg sound in air

e = v / c, phi - the direction of propagation

The equations are complicated, difficult to solve this.

But the problem may be simplified by applying transformations that just keep c (what is the transformation?).

We then obtain an equation identical with the case of stationary source that are already fairly easy to solve.

The whole mystery of the SR.