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Short Question: What is the reason that Doppler Effect in light is symmetric but asymmetric in sound?
Short Answer is summarised below:
In Sound, motion due to source affects the wavelength and the motion of the observer affects frequency. The relative velocity of the sound due to the motion of the observer is in the numerator. The relative velocity of sound due to motion of source is in denominator. The relative velocity of sound is not the same and constant.
In the case of doppler effect in light, first, the velocity of light is constant irrespective of the direction of motion of the observer or the source. There is no relative velocity.