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Relativity

The Relativistic Doppler Effect

Now consider A to be sending a continuous beam of electro-magnetic radiation (for example radio waves) rather than a series of pulses.

It is clear that each wave crest will have a little further to go than the preceding wave crest. So, as before, the interval between received crests will be greater than the interval between transmitted crests.

Now, if A and B both measure the frequency of the waves, B will obtain a lower frequency. We therefore have an effect which is very similar to the Doppler effect observed using sound waves.

It should be noted that there is a significant difference between the Doppler effect and the relativistic Doppler effect. In the mathematical analysis of the Doppler effect we consider the motion of observer and source relative to the medium (the air) through which the sound travels. The velocity of source and observer relative to the air can, of course, vary. It is now generally accepted that the "aether" does not exist and that all observers measure the velocity of electro-magnetic waves to be a constant, c. Hence, the mathematical analysis of the relativistic Doppler effect is fundamentally different from the Doppler effect in sound waves.

Rearranging the equation for relative velocity gives us

Note that if v is changed to -v, k changes to 1/k.

Now, as stated
which means that

the effect is usually expressed in the following way

This quantity is called the Doppler shift and can be written as

(fT - fR)/fT = 1 - (fR/fT) = 1 - 1/k

It can easily be shown that if v << c we have

Doppler shift =

Practical importance of the Relativistic Doppler Effect

1. The "red shift" of the light coming from distant galaxies gives direct evidence for the expanding universe theory.
2. The effect is used in the measurement of the speed of vehicles; especially cars and planes.

 

© David Hoult 2008