When the observer starts moving towards/away from the light source, both the frequency and the speed of the light (relative to him) change, in violation of Einstein's relativity:

http://www.youtube.com/watch?v=bg7O4rtlwEE
"Doppler effect - when an observer moves towards a stationary source. ...the velocity of the wave relative to the observer is faster than that when it is still."

http://www.youtube.com/watch?v=SC0Q6-xt-Xs
"Doppler effect - when an observer moves away from a stationary source. ...the velocity of the wave relative to the observer is slower than that when it is still."

Pentcho Valev