Question

A radar operates at wavelength $50.0cm$ If the beat frequency between the transmitted signal and the signal reflected from aircraft $\Delta v$ is $1kHz$, then velocity(in $km{h}^{-1}$ ) of the aircraft will be

Answer 1

Answer: 900

When source is fixed and observer is moving towards it
$v^{\prime }=\frac{c+a}{c}\times v$
When source is moving towards observer at rest
$v^{\prime \prime }=\frac{c}{c-a}{v}^{\prime }=\frac{c+a}{c-a}\times v=\frac{1+\frac{a}{c}}{1-\frac{a}{c}}v$
$=1+\frac{a}{c}1-{\frac{a^{-1}}{c}}^{-1}\approx 1+\frac{2a}{c}v$
$\therefore \Delta v=v^{\prime \prime }v=\frac{2av}{c}=\frac{2a}{\lambda }$
$\therefore a=\lambda \frac{\Delta v}{2}=\frac{0.5\times 1000}{2}=250m{s}^{-1}$
$=900km{h}^{-1}$