Relativistic Doppler effect.
There is an apparent shift in the observed frequency of any electromagnetic wave (light) when there is any relative motion between the source of light and the observer. This can be easily determined by using the 4-vector formulation of theory of relativity.
Lets discuss the details of this phenomena under two situations.
A. Source is at rest and observer is in motion.
Lets us consider two inertial frames S and S’. S’ is moving wrt S, along the x-axis with speed v = (beta) c where the observer is at rest in S’ frame but the source is at rest in the S frame.