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The speed of an electromagnetic wave is indeed independent of the speed of both the source and the receiver. However, this does not mean that the relative motion between the source and the receiver has no effect on the wave's properties. The effect that is being used is called the Doppler effect, and it is the fact that the received frequency of a wave will ...


1

This frame is exist. You got wrong result because you ignored that this two photon move in the opposite direction. Set that the first photon move along the z axis and the second photon move against z-axis.$\omega_1$ and $\omega_2$ are the frequency of the first and the second photon correspondingly in the reference frame. In new frame shout be $k'_1=-k'_2$ ...


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In fact, you do not have to find the frame $S'$ because the center of mass is independent of reference frame. It is $\sqrt{(h\nu_1+h\nu_2)^2-(h\nu_1-h\nu_2)^2}=2h\sqrt{\nu_1\nu_2}$.


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The 'Doppler Effect' applies specifically to the shift of frequency (or equivalently wavelength) of waves relative to the wave generator and an observer. The Doppler Effect can predict the shift of both sound waves and light waves, but doesn't predict any thing more than that. The wave mechanics of light and sound behave similarly in some respects to one ...


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It would appear to be correct. An example is a supersonic bullet fired over your head from a few hundred metres distance. You hear the crack of the bullet's shock wave as it passes, the sound of the round fired and (if your hearing is till up to it) the kind of sucking sound the bullet makes as it travels downrange. I imagine that a better setup would be to ...



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