The Doppler effect for sound waves is asymmetric, even though for the same relative motion in (i) and (ii) situations, the apparent shift in frequency is not the same. The explanation is that sound waves need a medium for their propagation, and the motion of the observer relative to the medium is different in two situations. That is why Doppler's formulas for sound are different in the two cases.
The Doppler effect is symmetrical for light waves, even though the same relative movement in case (i) and (ii). the apparent shift in frequency is same. The above two cases are similar in the case of light waves travelling in vaccum since the speed of light in vacuum is independent of the motion of the observer and the motion of the source(medium).
However, if light travels in a medium, the two situations above are not equivalent since the speed of light in a medium depends on the refractive index of that medium.
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https://www.youtube.com/watch?v=vDvIhiCnatE
https://www.youtube.com/watch?v=3mJTRXCMU6o