The frequency varies with the speed of the observer but in Divine Albert's schizophrenic world the wavelength also varies so that the speed of the waves relative to the observer can gloriously remain constant, Divine Einstein, yes we all believe in relativity, relativity, relativity:
http://highered.mcgraw-hill.com/olcweb/cgi/pluginpop.cgi?it=swf::800::600::/sites/dl/free/0072482621/78778/Doppler_Nav.swf "INTRODUCTION: Our ears detect changes in the frequency of sound waves due to the Doppler shift, but the waves change in another way, too: in their wavelength. Wavelength and frequency are closely related: if one increases, the other decreases. Their product, the speed of the wave, remains the same. The spaceship in this interactive has an instrument which detects electromagnetic radiation. You can see the wavelength and frequency change as the ship and the source of radiation move through space. EXERCISES: 2. Now click on the "Observer Approaches" button. The ship will start flying towards the source. What is the wavelength of the waves now, as the ship approaches the source? Does the frequency increase or decrease? SOLUTIONS: 2. The wavelength shrinks so that about three waves now fit within the graph. (...) The frequency increases."
http://www.pitt.edu/~jdnorton/teaching/HPS_0410/chapters/big_bang_observed/index.html John Norton: "Here's a light wave and an observer. If the observer were to hurry towards the source of the light, the observer would now pass wavecrests more frequently than the resting observer. That would mean that moving observer would find the frequency of the light to have increased (AND CORRESPONDINGLY FOR THE WAVELENGTH - THE DISTANCE BETWEEN CRESTS - TO HAVE DECREASED)."
http://www.imcce.fr/en/grandpublic/systeme/promenade/pages3/327.html "Décalage d'un spectre : l'effet Doppler. Cet effet se manifeste lorsque l'onde émise et l'observateur sont en mouvement l'un par rapport à l'autre et dans la direction de propagation de l'onde. L'observateur à l'arrêt voit passer 2 maxima consécutifs à chaque intervalle de temps t. S'il s'approche de la source de rayonnement, ce temps sera plus court. L'onde se manifestera avec une fréquence plus élevée, DONC UNE LONGUEUR D'ONDE PLUS COURTE."
Of course, the motion of the observer cannot change the wavelength (in a world different from Divine Albert's schizophrenic world) - it remains constant and therefore both the frequency and the speed of the waves vary with the speed of the observer, in violation of special relativity:
http://www.einstein-online.info/spotlights/doppler Albert Einstein Institute: "The frequency of a wave-like signal - such as sound or light - depends on the movement of the sender and of the receiver. This is known as the 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. 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."
That is, the motion of the observer cannot change the wavelength ("the distances between subsequent pulses are not affected") and accordingly the speed of light as measured by the receiver is (4/3)c.