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When you have a listener and a source, and when one of the two move relative to the other, the frequency perceived by the listener will be different.

Example:

  • If the listener travels toward the stationary source at 0.5 times the speed of sound, he will perceived a frequency 1.5 times higher.
  • If the source travels toward the stationary listener at 0.5 times the speed of sound, the listener will perceived a frequency 2 times higher.

I perfectly understand why the frequency is different in both cases (1.5 and 2 times): if you draw lines representing the crest of the cos wave emitted at a given frequency, you will see that the lines comes closer following the number I gave previously in the two cases.

What I don't understand is the Doppler effect for electromagnetic waves (like the light). Apparently the Doppler effect is there independent of who is moving and the only thing that matter is the relative velocity between the source and the receiver. I here only speak of non-relativistic Doppler effect so the relative speed is small with respect to the speed of light.

It can explain the red-shift of the star light due to the expansion of the universe.

Why is it only the relative speed that matter here? I read that it was because in the sound cases, the sound propagate in a medium (air) and that the light propagate in nothing ... but I do not see how it explains it ?

Thank you for any help !

Samuel.

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When you consider your example in terms of electromagnetic waves, relativistics comes into play. In this case it is time dilation. If you take time dilation into account, then the contradiction disappears. Let me show you:

If you consider yourself to be stationary and the emitter to be moving at 0.5c, then you will see the frequency 1.5 times higher. However time for the emitter has slowed. The frequency they emit is 1.155 higher than if it were at rest. The combined frequency you see is then 1.5 * 1.155 = 1.732 times higher than the emitter frequency.

Let's consider the other example, the emitter is stationary and you are moving at 0.5c. Doppler predicts the frequency to be twice is high. However since your time is 1.155 times slower, the frequency you see is, whaddoyaknow, only 2 / 1.155 = 1.732 times higher.

Exactly the same result, regardless of the refrence frame! Hooray for relativity!

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  • $\begingroup$ Thank you but I think it is the opposite: when you consider yourself to be stationary and the emitter to be moving at 0.5c, then you will see the frequency 2 times higher and the opposite? $\endgroup$
    – sponce
    Sep 28, 2013 at 17:18
  • $\begingroup$ Yes, you're correct. So I did the calculation the wrong way round. However I hope you see the point that when you consider time dilation the paradox disappears. $\endgroup$
    – Hannesh
    Sep 30, 2013 at 13:30

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