http://www.cmmp.ucl.ac.uk/~ahh/teaching/1B24n/lect19.pdf Tony Harker, University College London: "The Doppler Effect: Moving sources and receivers. The phenomena which occur when a source of sound is in motion are well known. The example which is usually cited is the change in pitch of the engine of a moving vehicle as it approaches. In our treatment we shall not specify the type of wave motion involved, and our results will be applicable to sound or to light. (...) Now suppose that the observer is moving with a velocity Vo away from the source. (....) If the observer moves with a speed Vo away from the source (...), then in a time t the number of waves which reach the observer are those in a distance (c-Vo)t, so the number of waves observed is (c-Vo)t/lambda, giving an observed frequency f'=f(1-Vo/c) when the observer is moving away from the source at a speed Vo."
If "in a time t the number of waves which reach the observer are those in a distance (c-Vo)t", then the speed of the light waves relative to the observer is:
c' = ((c - Vo)t)/t = c - Vo
in violation of special relativity. The frequency measured by the moving observer is: