Then the source and the observer start moving towards each other with (small) relative speed v - the measured frequency shifts from f=c/d to f'=(c+v)/d.
According to the Albert Einstein Institute, the scenarios "Moving source" and "Moving observer" are different. If the source starts moving towards the stationary observer, and if we assume that the speed of the pulses relative to the observer remains constant, then the distance between subsequent pulses decreases, and this shift in distance (from d to d'=c/f') causes the frequency shift measured by the observer:
http://www.einstein-online.info/spotlights/doppler "Next, let us look at a slightly different situation, where the source is moving towards the detector. We assume that the motion of the sender does not influence the speed at which the pulses travel, and that the pulses are sent with the same frequency as before. Still, as we can see in the following animation, the motion influences the pulse pattern: The distance between successive pulses is now smaller than when both sender and receiver were at rest. Consequently, the pulses arrive at the receiver in quicker succession."
If it is the observer that starts moving towards the stationary source, the distance between subsequent pulses is not affected (d'=d) and therefore the frequency shift measured by the observer can only be caused by a shift in the speed of the pulses relative to the observer (from c to c'=c+v):
http://www.einstein-online.info/spotlights/doppler "Here is an animation of the receiver moving towards the source (...) By observing the two indicator lights, you can see for yourself that, once more, there is a blue-shift - the pulse frequency measured at the receiver is somewhat higher than the frequency with which the pulses are sent out. This time, the distances between subsequent pulses are not affected, but still there is a frequency shift: As the receiver moves towards each pulse, the time until pulse and receiver meet up is shortened. In this particular animation, 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."
Clearly the interpretation of the Albert Einstein Institute contradicts the principle of relativity. More precisely, the constant-speed-of-light assumption made in the "Moving source" scenario - "We assume that the motion of the sender does not influence the speed at which the pulses travel" - is irreconcilable with the principle of relativity and therefore false.
The lie embodied in the words "only apparently" in Einstein's 1905 paper has proved to be the most devastating lie in the history of science:
http://www.fourmilab.ch/etexts/einstein/specrel/www/ ON THE ELECTRODYNAMICS OF MOVING BODIES, A. Einstein, 1905: "We will raise this conjecture (the purport of which will hereafter be called the "Principle of Relativity'') to the status of a postulate, and also introduce another postulate, which is only apparently irreconcilable with the former, namely, that light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body."