# Relativistic Doppler Effect

*Most recent answer: 08/20/2018*

Q:

So I was thinking about the idea that light moves at a constant speed no matter which reference frame it's viewed from, and it struck me that I'm not sure how that functions with respect to the Doppler effect. If the light producing object is moving away at a high speed, does the speed of light with respect to another observer stay constant while the wavelength is altered? How does that work? You'd expect the speed of light to slow from the observer's perspective.

- Harry (age 18)

- Harry (age 18)

A:

You're right that the relativistic Doppler effect has to be a little different from the classical one. The speed of light does remain constant as seen by any observer, contrary to our classical intuition. The frequency changes by a factor (1+v/c)^{1/2}/(1-v/c)^{1/2 }, not the classical (1+v/c), where v is positive for an approaching source and negative for one going away. The relativistic Doppler shift gives the same factor for a source approaching the detector or for the detector approaching the source. Only the relative velocity matters. The classical formula doesn't, because it matters which of them is moving with repect to the classical medium.

Mike W.

*(published on 08/20/2018)*