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  4. The frequency of a radar is 780 MHz. The frequency of reflected wave from aeroplane is increased by 2.6 kHz. Velocity of the aeroplane is :

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Q. The frequency of a radar is $780\, MHz$. The frequency of reflected wave from aeroplane is increased by $2.6\, kHz$. Velocity of the aeroplane is :

J & K CETJ & K CET 2001

Solution:

The velocity of aero plane $v=\frac{1}{2} \frac{\Delta n c}{n}$
Given, $\Delta n=2.6 \,kHz =2.6 \times 10^{3} Hz$,
$c=3 \times 10^{8} m / s $,
$ n=780 \,MHz =780 \times 10^{6} Hz $
$v=\frac{1}{2} \frac{2.6 \times 10^{3} \times 3 \times 10^{8}}{780 \times 10^{6}}$
$v=0.5 \times 10^{3} m / s $
$v=0.5 \,km / s$