In the case of light, the Doppler effect cannot distinguish whether the source or the observer is moving, only that they are approaching each other or separating from each other. The idea resolving this paradox was pointed out by Einstein time dilation: when the source or the observer moves, their internal clocks slow down, an effect noticeable as speeds approach the speed of light. However, in the case of light in a classical vacuum, according to special relativity one cannot detect the medium, so the Doppler shift cannot be given by the above formula.
But if they are in uniform straight-line motion toward one another, should it be possible to distinguish which object was moving? The answer is "yes, we can tell the difference" in the case where a medium is involved like air or water, because the medium introduces a third reference frame, and the discussion above is made in the frame of the medium. It would appear that careful observation of the Doppler effect could distinguish between movement of the source and that of the observer. In that case, the time between crests for an observer at a fixed location is λ / c, and the frequency with which a crest appears at a fixed location is f w :į w = 1 λ / c = c λ. Suppose that waves blowing ashore with velocity c are spaced a distance λ apart. The increase in frequency when moving toward a source can be explained using the figure.
Boat traveling against waves experiences Doppler effect.
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