The question "If light speed is constant, how do you explain the Doppler Effect?" has been asked a lot in the internet. Anyway, I haven't found one concise answer. In the book Kleppner&Kolenkow Mechanics there is a brief explanation of the Relativistic Doppler Effect, but as usual in this topic, it uses the property of light speed being constant to explain it (it doesn't deduce this last property). So, the right questions to ask, in my opinion are these: How would you (cleverly) use the red shift property to deduce that light speed is constant? In terms of the properties of light as a wave, what happens to the wave in order to change it's wavelength to red but maintain it's speed.