Question

A traffic policeman sounds a whistle to stop a car-driver approaching towards him. The car-driver does not stop and takes the plea in court that because of the Doppler shift, the frequency of the whistle reaching him might have gone beyond the audible limit of 20 kHz and he did not hear it, Experiments showed that the whistle emits a sound with frequency close to 16 kHz. Assuming that the claim of the driver is true, how fast was he driving the car? Take the speed of sound in air to be $330m{s}^{-1}$.

• A. 297 km/hr
• B. 297 km/hr
• C. 330 km/hr
• D. 150 km/hr

Answer 1

The correct option is A 297 km/hr

Here given $f_s=16\times {10}^3$ Hz

Apparent frequency $f^{\prime }=20\times {10}^{3}Hz$ (greater than that value)

Let the velocity of the observer =$v_0$

Given $v_s$ = 0

So $20\times {10}^3=\left(\frac{330+v_0}{330-0}\right)\times 16\times {10}^3$

$\Rightarrow (330+v_0)=\frac{20\times 330}{16}$

$\Rightarrow v_0=\frac{20\times 330-16\times 330}{4}=\frac{330}{4}m/s=297km/h$