If light from a galaxy observed on the earth's surface has a red shift,then:

Apparent wavelength of light coming from a star moving away from Earth is $0.02 \%$ more than its actual wavelength. The velocity of the star is ........ $km/s$.

If a star is moving towards the Earth,then the spectral lines are shifted towards:

$A$ star moves away from Earth at a speed of $0.8 c$ while emitting light of frequency $6 \times 10^{14} \text{ Hz}$. What frequency will be observed on the Earth (in units of $10^{14} \text{ Hz}$)? ($c$ is the speed of light)

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?

With what speed should a galaxy move outward with respect to Earth so that the sodium-$D$ line at wavelength $5890 \ \mathring{A}$ is observed at $5896 \ \mathring{A}$? (in $\text{km/s}$)