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Wave Optics — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsWave Optics3 Marks
Question
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?
✓

Answer

Sound waves require a medium for propagation. Thus, even though both the situations may correspond to the same relative motion (between the source and the observer), they are not identical physically since, the motion of the observer, relative to the medium is different in the two situations. Therefore, we cannot expect Doppler formulas for sound to be identical for (i) and (ii).
For light waves in vacuum, there is clearly nothing to distinguish between two cases given. Here only the relative motion between the source and the observer counts and the relativistic Doppler formula is the same for both cases. For light propagation in a medium, once again like for sound waves, the two situations are not identical and we should expect the Doppler formulas for this case to be different for the two situations (i) and (ii).

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