Relativistic Doppler Effect

Friday, November 02, 2018

Relativistic Doppler Effect

The Relativistic Doppler Effect

The relativistic Doppler effect occurs when there is relative motion between a source of waves and an observer.

You can understand the basic idea behind the Doppler effect when you think about sound waves. As the source comes towards you the waves pile up and have a higher frequency and so are higher pitched. This is heard when a car passes you. The engine sounds high pitched as the car approaches you and after it passes you, the pitch decreases as the waves become more spread out.

So if we have light from a source and we want to know the frequency at which it is measured by a moving observer.

The equation above is the equation for the relativistic Doppler Effect.

If the source is going away from you like in the example. v is positive, √(1-(v/c)/1+(v/c) is less than one and so the frequency measured by the observer is less than the frequency emitted. If the source is coming towards you, then the velocity is negative and so the frequency measured is greater than the frequency of the waves from the source.

This will be useful in looking at the another version of the twin paradox where the Twins have telescopes and can see each other. Will both twins see each other age slowly the whole time? Will only one twin see the other age slowly while the other ages normally? Will one twin suddenly age when one undergoes the acceleration to turn around? The relativistic Doppler effect will allow us to answer these questions.

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