10.15 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 a vacuum are, however, strictly identical for these situations. Explain why this should be so. Would you expect the formulas to be strictly identical to the two situations in the case of light traveling in a medium?

Doppler effect for sound waves is asymmetric i.e. for the same relative motion in the cases (i) and (ii), the apparent change in the frequency is not the same. It is because, sound waves require a medium for their propagation and the motion of the observer relative to the medium is different in two cases. Doppler effect for light waves is symmetric i.e. for the same relative motion in the case (i) and (ii), the apparent change in the frequency is same. For light waves in vacuum, there is no difference in the two cases. It is because, the relative motion between the source and the observer is not affected, whether the source is in motion or the observer is in motion. However, for the light waves in medium, the situations in the two cases are different as in the case of Doppler effect for sound waves. Likewise the formulas for Doppler effect in the two cases will be different.Read more on Sarthaks.com - https://www.sarthaks.com/634456/for-sound-waves-the-doppler-formula-frequency-shift-differs-slightly-between-situations
Doppler effect for sound waves is asymmetric i.e. for the same relative motion in the cases (i) and (ii), the apparent change in the frequency is not the same. It is because, sound waves require a medium for their propagation and the motion of the observer relative to the medium is different in two cases. Doppler effect for light waves is symmetric i.e. for the same relative motion in the case (i) and (ii), the apparent change in the frequency is same. For light waves in vacuum, there is no difference in the two cases. It is because, the relative motion between the source and the observer is not affected, whether the source is in motion or the observer is in motion. However, for the light waves in medium, the situations in the two cases are different as in the case of Doppler effect for sound waves. Likewise the formulas for Doppler effect in the two cases will be different.Read more on Sarthaks.com - https://www.sarthaks.com/634456/for-sound-waves-the-doppler-formula-frequency-shift-differs-slightly-between-situationsDoppler effect for sound waves is asymmetric i.e. for the same relative motion in the cases (i) and (ii), the apparent change in the frequency is not the same. It is because, sound waves require a medium for their propagation and the motion of the observer relative to the medium is different in two cases. Doppler effect for light waves is symmetric i.e. for the same relative motion in the case (i) and (ii), the apparent change in the frequency is same. For light waves in vacuum, there is no difference in the two cases. It is because, the relative motion between the source and the observer is not affected, whether the source is in motion or the observer is in motion. However, for the light waves in medium, the situations in the two cases are different as in the case of Doppler effect for sound waves. Likewise the formulas for Doppler effect in the two cases will be different.Read more on Sarthaks.com - https://www.sarthaks.com/634456/for-sound-waves-the-doppler-formula-frequency-shift-differs-slightly-between-situationsDoppler effect for sound waves is asymmetric i.e. for the same relative motion in the cases (i) and (ii), the apparent change in the frequency is not the same. It is because, sound waves require a medium for their propagation and the motion of the observer relative to the medium is different in two cases. Doppler effect for light waves is symmetric i.e. for the same relative motion in the case (i) and (ii), the apparent change in the frequency is same. For light waves in vacuum, there is no difference in the two cases. It is because, the relative motion between the source and the observer is not affected, whether the source is in motion or the observer is in motion. However, for the light waves in medium, the situations in the two cases are different as in the case of Doppler effect for sound waves. Likewise the formulas for Doppler effect in the two cases will be different.Read more on Sarthaks.com - https://www.sarthaks.com/634456/for-sound-waves-the-doppler-formula-frequency-shift-differs-slightly-between-situationsDoppler effect for sound waves is asymmetric i.e. for the same relative motion in the cases (i) and (ii), the apparent change in the frequency is not the same. It is because, sound waves require a medium for their propagation and the motion of the observer relative to the medium is different in two cases. Doppler effect for light waves is symmetric i.e. for the same relative motion in the case (i) and (ii), the apparent change in the frequency is same. For light waves in vacuum, there is no difference in the two cases. It is because, the relative motion between the source and the observer is not affected, whether the source is in motion or the observer is in motion. However, for the light waves in medium, the situations in the two cases are different as in the case of Doppler effect for sound waves. Likewise the formulas for Doppler effect in the two cases will be different.Read more on Sarthaks.com - https://www.sarthaks.com/634456/for-sound-waves-the-doppler-formula-frequency-shift-differs-slightly-between-situations

Hint: Doppler effect for sound waves is asymmetric.

Step 1: Analyse the Doppler effect for sound waves.
For the same relative motion in cases (i) and (ii), the apparent change in the frequency is not the same. It is because sound waves require a medium for their propagation and the motion of the observer relative to the medium is different in the two cases.

Step 2: Analyse the Doppler effect for light waves.
Doppler effect for light waves is symmetric i.e. for the same relative motion in the case (i) and (ii), the apparent change in the frequency is the same. For light waves in a vacuum, there is no difference in the two cases. It is because the relative motion between the source and the observer is not affected, whether the source is in motion or the observer is in motion. However, for the light waves in a medium, the situations in the two cases are different as in the case of the Doppler effect for sound waves. Likewise, the formulas for the Doppler effect in the two cases will be different.