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 $330 \,m / s$. Is this speed (in $km / hr$ ) practical with today's technology ?

Answer 1

Let speed of the car be $u$
Speed of sound in air $=v=330 \,m / s$
Frequency of sound emitted by whistle
$=v=16 \times 10^{3}\, Hz$
Frequency of sound emitted by
car driver $\geq 20 \times 10^{3} \,Hz$
As $ v'=\frac{v+u}{v} v$
$20 \times 10^{3} =\left(\frac{330+u_{\min }}{330}\right) \times 16 \times 10^{3} $
$\frac{5}{4} \times 330 =330+u_{\min } $
$u_{\min } =\frac{1}{4} \times 330=82.5\, m / s$
$ \approx 297\, km / h$
So this speed is possible with today's technology.