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Albert Einstein Institute: "...Doppler...the receiver moving towards the source...the distances between subsequent pulses are not affected, but still there is a frequency shift..." http://einstein-online.info/spotlights/doppler.html
This entails that the speed of the light pulses relative to the receiver VARIES, in accordance with the formula
(frequency) = (speed of pulses)/(distance between pulses)
This particular variation of the speed of light is obvious:
The speed of the light pulses relative to the stationary observer is
c = df
where d is the distance between the pulses and f is the frequency measured by the stationary observer. The speed of the pulses relative to the moving observer is
c'= df' > c
where f' > f is the frequency measured by the moving observer.