I understand Doppler effect in Sound and Water because there we can observe relative speeds. But in case of light, the speed is same in all references so is the change in relative wavelength due to the inability to change relative velocity?
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1$\begingroup$ By applying the Lorentz transform to the argument of the wavefunction. The wavelength and frequency increase and decrease respectively (for redshift) by the same factor. So the wavespeed is constant. $\endgroup$– ProfRobCommented Apr 3, 2016 at 18:19
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$\begingroup$ So the shift is just because there can't be a change in speed, right? $\endgroup$– Prabhdeep SinghCommented Apr 3, 2016 at 18:21
2 Answers
Doppler's effect works exactly same way for all waves. I.e. Same number of pulses have to cover more, or less distance depending upon the relative speed of source away from, or towards the observer. This is because, the speed is constant.
"is the change in relative wavelength due to the inability to change relative velocity?"
There is no change in wavelength, and in the case of moving observer (receiver) this is obvious:
http://www.einstein-online.info/spotlights/doppler Albert Einstein Institute: "The frequency of a wave-like signal - such as sound or light - depends on the movement of the sender and of the receiver. This is known as the Doppler effect. (...) Here is an animation of the receiver moving towards the source:
http://www.einstein-online.info/images/spotlights/doppler/doppler_detector_blue.gif
By observing the two indicator lights, you can see for yourself that, once more, there is a blue-shift - the pulse frequency measured at the receiver is somewhat higher than the frequency with which the pulses are sent out. This time, THE DISTANCES BETWEEN SUBSEQUENT PULSES ARE NOT AFFECTED, but still there is a frequency shift: As the receiver moves towards each pulse, the time until pulse and receiver meet up is shortened. In this particular animation, which has the receiver moving towards the source at one third the speed of the pulses themselves, four pulses are received in the time it takes the source to emit three pulses."
Since "four pulses are received in the time it takes the source to emit three pulses", the speed of the pulses relative to the receiver is greater than their speed relative to the source, in violation of Einstein's relativity.
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$\begingroup$ Why 2 downvotes, and no explanation? $\endgroup$– user104372Commented Sep 18, 2016 at 9:55