![]() ![]() In this example, the light always propagates in the same direction, and only the separation of the observer and source is changing. A Doppler effect is seen for stars even when they are in a plane perpendicular to the line of sight, because of the transverse Doppler effect predicted by special relativity. Īs for binary stars, the case considered by Doppler, as the stars orbit each other, they are alternately moving toward and away from the observing astronomer, so the frequency of the light from each star (its color) alternates as well. The same effect appears when the ear and a police siren move toward each other: the sound of the siren to the ear is pitched higher than the actual frequency of the siren, and when the police pass, so the ear and siren are separating, and the waves from the siren are traveling in the same direction as the ear, the pitch to the ear drops to become lower than the frequency of the siren. Īn interesting corollary of special relativity is that there is a transverse Doppler effect for light emitted in vacuum, that is, a Doppler effect is present even for an observation perpendicular to the motions of source or observer, sometimes called the second-order Doppler effect because it is of second order, varying as (v/c) 2 ( c the speed of light in classical vacuum). Consequently light in classical vacuum is a special case. 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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