http://www.aip.org/history/einstein/essay-einstein-relativity.htm John Stachel: "But here he ran into the most blatant-seeming contradiction, which I mentioned earlier when first discussing the two principles. As noted then, the Maxwell-Lorentz equations imply that there exists (at least) one inertial frame in which the speed of light is a constant regardless of the motion of the light source. Einstein's version of the relativity principle (minus the ether) requires that, if this is true for one inertial frame, it must be true for all inertial frames. But this seems to be nonsense. How can it happen that the speed of light relative to an observer cannot be increased or decreased if that observer moves towards or away from a light beam?"
The frequency the moving observer measures is:
f'=(c+v)/L or f'=(c-v)/L
where v is the speed of the observer relative to the light source and L is the wavelength.
For all waves other the light waves, the following formula is valid:
where c' is the speed of the waves relative to the moving observer. Sane scientists know that the formula f'=c'/L is valid for ALL waves, light waves included:
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://physics.bu.edu/~redner/211-sp06/class19/class19_doppler.html Sidney Redner: "The Doppler effect is the shift in frequency of a wave that occurs when the wave source, or the detector of the wave, is moving. Applications of the Doppler effect range from medical tests using ultrasound to radar detectors and astronomy (with electromagnetic waves). (...) We will focus on sound waves in describing the Doppler effect, but it works for other waves too. (...) 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'/(lambda)=(v+vO)/(lambda)."
http://www.usna.edu/Users/physics/mungan/Scholarship/DopplerEffect.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, so that we expect v'>v. 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. Thus, v'=v+v_o=v(1+v_o/v). Finally, the frequency must increase by exactly the same factor as the wave speed increased, in order to ensure that L'=L -> v'/f'=v/f. Putting everything together, we thus have: OBSERVER MOVING TOWARD SOURCE: L'=L; f'=f(1+v_o/v); v'=v+v_o."
http://www.phys.uconn.edu/~gibson/Notes/Section6_3/Sec6_3.htm Professor George N. Gibson, University of Connecticut: "However, if either the source or the observer is moving, things change. This is called the Doppler effect. (...) To understand the moving observer, imagine you are in a motorboat on the ocean. If you are not moving, the boat will bob up and down with a certain frequency determined by the ocean waves coming in. However, imagine that you are moving into the waves fairly quickly. You will find that you bob up and down more rapidly, because you hit the crests of the waves sooner than if you were not moving. So, the frequency of the waves appears to be higher to you than if you were not moving. Notice, THE WAVES THEMSELVES HAVE NOT CHANGED, only your experience of them. Nevertheless, you would say that the frequency has increased. Now imagine that you are returning to shore, and so you are traveling in the same direction as the waves. In this case, the waves may still overtake you, but AT A MUCH SLOWER RATE - you will bob up and down more slowly. In fact, if you travel with exactly the same speed as the waves, you will not bob up and down at all. The same thing is true for sound waves, or ANY OTHER WAVES. (...) The formula for the frequency that the observer will detect depends on the speed of the observer; the larger the speed the greater the effect. If we call the speed of the observer, Vo, the frequency the observer detects will be: f'=f(1+Vo/Vwave). Here, f is the original frequency and Vwave is the speed of the wave."
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."