For sound waves, the Doppler formula for frequency shift differs slightly between the two situations: (i) source at rest, observer moving and (ii) source moving, observer at rest. The exact Doppler formulas for the case of light waves in vacuum are, however strictly identical for these situations. Explain why this should be so. Would you expect the formulas to be strictly identical for the two situations in case of light travelling in a medium?

Explanation

Sound requires a material medium for it propagation. The relative motion of source and listener, need not be identical. In vacuum, light has the same speed irrespective of motion of source and observe-hence results of Doppler effect are identical. But in a medium, light produces Doppler effect similar to sound.