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I am little bit confused about the formula for the transverse Doppler shift( whether we use relativity or not, it isn't relevant to what I am about to ask) because I tried to derive it myself and I found out that the well known formula : $$\nu = \nu_0 \bigg( 1-\frac{v \cdot cos\theta}{c}\bigg)^{-1} $$ is actually an aproximation... ( the formula above is for a source , its direction of motion making an angle (theta) with the direction to the detector)

I think that it makes sense that this formula is applicable only for large distances to the detector( or very high frequencies), because if we were to have a shorter distance to the detector relative to the distance travelled by the source during one period, than the angle theta will change.

Am I right?

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A "transverse Doppler effect" exists only in relativistic not in classical physics! See Relativistic Doppler Effect

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  • $\begingroup$ Ok than, let's consider the Relativistic Doppler Effect. Same question: "I think that it makes sense that this formula is applicable only for large distances to the detector( or very high frequencies), because if we were to have a shorter distance to the detector relative to the distance travelled by the source during one period, than the angle theta will change. Am I right?" $\endgroup$
    – CosminA
    Commented Feb 14, 2017 at 19:54

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