The Doppler effect is applicable for

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?

$A$ heavenly body is receding from Earth such that the fractional change in wavelength $\lambda$ is $1$. What is its velocity?

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 $\text{km/s}$)

Due to the Doppler effect,the shift in wavelength observed is $0.1\;\mathring{A}$,for a star producing a wavelength of $6000\;\mathring{A}$. The velocity of recession of the star will be ....... $km/s$.

The $K$ line of singly ionised calcium has a wavelength of $393.3 \, nm$ as measured on Earth. In the spectrum of one of the observed galaxies,this spectral line is located at $401.8 \, nm$. The speed with which the galaxy is moving away from us will be..... $km/s$.