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If a wave source and observer are moving with the same velocity, then the movement of the wave source is supposed to result in a change of frequency and wavelength, whereas the movement of the observer is supposed to result in a change in the observed frequency and velocity of the wave.

The math shows (at least in the case of 1 dimensional motion) that the final observed frequency is the same as when the wave source and observer are stationary, but what about the observed velocity and wavelength? Are they both the same as when both source and observer are stationary, or different (such that the observed velocity is different due to observer motion, and observed wavelength is different due to source motion)?

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    $\begingroup$ The answer to your question is dependent on the wave. Sound in air and light in spacetime are different. Also: it's usually simpler to transform wavenumber, $k$, than wavelength (but that is my personal bias from woking in spaceborne radar). $\endgroup$
    – JEB
    Oct 21, 2019 at 12:52

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The velocity, wavelength and frequency is related by the equation V=f√ Where V=Velocity f = frequency √ = wavelength I'm case of Dopplers Effect, if the source and the observer are moving with the same Velocity then there is no relative motion hence the observer observes the same frequency as emitted by the source, therefore we can say that the wavelength and Velocity change in such a way that the frequency remains constant

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