http://www.einstein-online.info/spotlights/doppler

Albert Einstein Institute: "In the above paragraphs, we have only considered moving sources. In fact, a closer look at cases where it is the receiver that is in motion will show that this kind of motion leads to a very similar kind of Doppler effect. 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."

That is, the frequency measured at the receiver, f', is higher than f, the frequency measured at the source. The wavelength measured at the receiver, L', is equal to L, the wavelength measured at the source. Therefore, the speed of light measured at the receiver, c', is higher than c, the speed of light measured at the source:

c' = L'f' > Lf = c

See also:

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.expo-db.be/ExposPrecedentes/ ... oppler.pdf

"La variation de la fréquence observée lorsqu'il y a mouvement relatif entre la source et l'observateur est appelée effet Doppler. (...) 6. Source immobile - Observateur en mouvement: La distance entre les crêtes, la longueur d'onde lambda ne change pas. Mais la vitesse des crêtes par rapport à l'observateur change !"

http://www.usna.edu/Users/physics/munga ... Effect.pdf

Carl Mungan: "Consider the case where the observer moves toward the source. In this case, the observer is rushing head-long into the wavefronts... (...) In fact, the wave speed is simply increased by the observer speed, as we can see by jumping into the observer's frame of reference."

http://www.hep.man.ac.uk/u/roger/PHYS10 ... ture18.pdf

Roger Barlow, Professor of Particle Physics: "Moving Observer. Now suppose the source is fixed but the observer is moving towards the source, with speed v. In time t, ct/(lambda) waves pass a fixed point. A moving point adds another vt/(lambda). So f'=(c+v)/(lambda)."

http://www.cmmp.ucl.ac.uk/~ahh/teaching ... lect19.pdf

Tony Harker, University College London: "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((c-Vo)/c) when the observer is moving away from the source at a speed Vo."

Pentcho Valev

pvalev@yahoo.com

http://physics.bu.edu/~duffy/py105/Doppler.html

Boston University: "The Doppler effect describes the shift in the frequency of a wave sound when the wave source and/or the receiver is moving. We'll discuss it as it pertains to sound waves, but the Doppler effect applies to any kind of wave. (...) If the observer is stationary, the frequency received by the observer is the frequency emitted by the source: observed frequency (everything stationary): f=v/(lambda) (v = speed of sound). If the observer moves toward the source at a speed vo, more waves are intercepted per second and the frequency received by the observer goes up. Effectively, the observer's motion shifts the speed at which the waves are received; it's basically a relative velocity problem. The observed frequency is given by: observed frequency, moving observer: f'=(v+vo)/(lambda)."

If vo is low enough, the above result is equally valid for light waves (as explained in textbooks, relativistic corrections are negligible): f'=(c+vo)/(lambda). Moreover, the author clearly suggests that the analysis "applies to any kind of wave". Yet the statement "the observer's motion shifts the speed at which the waves are received" is obviously fatal for Einstein's special relativity.

Let us assume that I am somewhat exaggerating and the author does not suggest that the analysis applies to light vaves. Still a huge problem remains: the correct formula f'=(c+vo)/(lambda), combined with the correct formula f'=c'/(lambda)', leads to the following reasonable conclusion:

c' = c + vo ; (lamda)' = (lamda)

If Einsteinians wish to save special relativity, they will have to extract an alternative, much more reasonable, conclusion from the correct formulas f'=(c+vo)/(lambda) and f'=c'/(lambda)'.

Pentcho Valev

pvalev@yahoo.com