Date: Dec 9, 2012 2:45 AM
Author: Pentcho Valev

Textbooks correctly teach that, for all waves, if the observer starts moving towards the wave source with speed v and if v is low enough, the frequency as measured by the observer shifts from f to f'=f(1+v/c). This implies that, relative to the observer, the speed of the waves shifts from c to c'=c+v. The implication is extremely dangerous when applied to light waves (it leaves modern physics in ruins) so prudent authors avoid it. Here are some examples of careless authors who don't see the danger:
Fang-Yuh Lo, Department of Physics, National Taiwan Normal University: "Observer moves toward source: frequency becomes higher. Observer moves away from source: frequency becomes lower. How much higher (lower)? Wavelength does not change. Change in velocity: Vnew=Vwave±Vobs."
"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."
"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 !"
Professor Sidney Redner: "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)."
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)."
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