In the hydrogen spectrum,the wavelength of the ${H_\alpha}$ line is $656 \ nm$,whereas in the spectrum of a distant galaxy,the ${H_\alpha}$ line wavelength is $706 \ nm$. The estimated speed of the galaxy with respect to the Earth is:

The $6563 \ \mathring{A}$ line emitted by a hydrogen atom in a star is found to be red-shifted by $5 \ \mathring{A}$. The speed with which the star is receding from the Earth is:

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?

Light from the constellation Virgo is observed to increase in wavelength by $0.4\%$. With respect to Earth,the constellation is:

$A$ spectral line $\lambda = 5000\ \mathring A$ in the light coming from a distant star is observed as $5200\ \mathring A$. What will be the recession velocity of the star?

The observed wavelength of light coming from a distant galaxy is found to be increased by $0.5\%$ as compared with that coming from a terrestrial source. The galaxy is