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The equation of a travelling sine wave is given by $$y=Asin(wt-kx)$$ On seeing this from a different reference frame,we use galilean transformation,where,in new frame,replacing x by x-vt,the new equation is, $$y=Asin(w't-kx)$$ Where$$w'=w+kv$$ So,the frequency gets changed,not wavelength.

  • But DOPPLER EFFECT says that for a moving observer wavelength of the wave changes.Where lies the problem?
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What you've described is the case when the observer is moving. It's true that in this case, wavelength has no change, but frequency and wavespeed are changed.

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