A radar sends radio waves of frequency ν towards an aeroplane moving with velocity va…

Q: A radar sends radio waves of frequency ν towards an aeroplane moving with velocity va .  A change Δν is observed in the frequency of reflected waves which is higher than original frequency. The velocity of aeroplane is (va ≪ c)

(a) va = (c Δν)/ν

(b) va = (2 c ν)/Δν

(c) va = (c Δν)/(2 ν)

(d) va = (Δν)/(2 c ν)

Ans: (c)

Sol: $ \displaystyle v_a = \frac{1}{2} \frac{\Delta \nu}{\nu} \times c $