A radar sends radio waves of frequency $\nu$ towards an aeroplane moving with velocity $v_A$. A change…
A radar sends radio waves of frequency $\nu$ towards an aeroplane moving with velocity $v_A$. A change $\Delta\nu$ is observed in the frequency of reflected wave which is higher than the original frequency. The velocity of aeroplane ($v_A \ll c$) is [CG PMT 2015]
$c \frac{\Delta\nu}{\nu}$
$2 \frac{c\nu}{\Delta\nu}$
$c \frac{\Delta\nu}{2\nu}$
$\frac{\Delta\nu}{2c\nu}$
Solution
Since, the Doppler shift affects the wave incident upon the aeroplane as well as the wave reflected back to the radar, change in frequency observed by a radar due to an aeroplane moving at relative velocity $v_A$ (given) is twice than that from the aeroplane emitting the wave, i.e.
$\Delta\nu = 2 \cdot \frac{v_A}{c} \nu$
Therefore, the velocity of aeroplane, $v_A = c \frac{\Delta\nu}{2\nu}$