When the observer starts moving towards the light source with speed v, the frequency he measures shifts from f=c/λ to f'=(c+v)/λ=f(1+v/c):

http://www.hep.man.ac.uk/u/roger/PHY.../lecture18.pdf
"The Doppler effect - changes in frequencies when sources or observers are in motion - is familiar to anyone who has stood at the roadside and watched (and listened) to the cars go by. It applies to all types of wave, not just sound. [...] Moving Observer. Now suppose the source is fixed but the observer is moving towards the source, with speed v. In time t, ct/λ waves pass a fixed point. A moving point adds another vt/λ. So f'=(c+v)/λ."

http://docplayer.net/35188128-Modern...ecture-35.html
"Now let's see what this does to the frequency of the light. We know that even without special relativity, observers moving at different velocities measure different frequencies. (This is the reason the pitch of an ambulance changes as it passes you it doesn't change if you're on the ambulance). This is called the Doppler shift, and for small relative velocity v it is easy to show that the frequency shifts from f to f(1+v/c) (it goes up heading toward you, down away from you). There are relativistic corrections, but these are negligible here."

Does this mean that the speed of the light relative to the observer shifts from c to c'=c+v? Yes. Consider the following setup:

A light source emits a series of pulses equally distanced from one another. A stationary observer (receiver) measures the speed of the pulses to be c and the frequency to be f=c/d, where d is the distance between the pulses:

http://www.einstein-online.info/imag...ler_static.gif

The observer starts moving with constant speed v towards the light source - the frequency he measures shifts from f=c/d to f'=(c+v)/d:

http://www.einstein-online.info/imag...ector_blue.gif

The following formula is correct:

f' = c'/d

where c' is the speed of the pulses as measured by the moving observer. Clearly,

c' = c + v.

That is, the speed of the pulses varies with the speed of the observer, in violation of Einstein's relativity. Any correct interpretation of the Doppler effect unavoidably leads to the same conclusion:

http://physics.bu.edu/~redner/211-sp...9_doppler.html
"Let's say you, the observer, now move toward the source with velocity vo. You encounter more waves per unit time than you did before. Relative to you, the waves travel at a higher speed: v'=v+vo. The frequency of the waves you detect is higher, and is given by: f'=v'/λ=(v+vo)/λ."

http://a-levelphysicstutor.com/wav-doppler.php
"vo is the velocity of an observer moving towards the source. This velocity is independent of the motion of the source. Hence, the velocity of waves relative to the observer is c + vo. [...] The motion of an observer does not alter the wavelength. The increase in frequency is a result of the observer encountering more wavelengths in a given time."

http://www.einstein-online.info/spotlights/doppler
Albert Einstein Institute: "In this particular animation

http://www.einstein-online.info/imag...ector_blue.gif

which has the receiver moving towards the source at one third the speed of the pulses themselves, four pulses are received in the time it takes the source to emit three pulses." [end of quotation]

Since "four pulses are received in the time it takes the source to emit three pulses", the speed of the pulses relative to the receiver (observer) is greater than their speed relative to the source, in violation of Einstein's relativity.

Pentcho Valev