A traffic policeman blows a whistle to halt an approaching car-driver. The car-driver fails to stop and later argues in court that, due to the Doppler shift, the frequency of the whistle reaching him could have exceeded

Question

Quantrex Academy · Accepted Answer

Correct answer: D. 297 km/h

The frequency heard by the approaching driver is given by the Doppler effect formula:

f' = f \left( \dfrac{v + v_c}{v} \right)<br><br>where

f' is the apparent frequency,

f

is the actual frequency,

v

is the speed of sound, and

v_c

is the speed of the car.

Given

f' = 20

\text{ kHz},

f = 16

\text{ kHz}, and

v = 330

\text{ m s}^{-1}, substituting these values:

20 = 16 \left( \dfrac{330 + v_c}{330} \right)

\dfrac{5}{4} = 1 + \dfrac{v_c}{330}

\dfrac{v_c}{330} = \dfrac{1}{4}

v_c = \dfrac{330}{4} = 82.5 \text{ m s}^{-1}

Converting the speed from

\text{m s}^{-1}

to

\text{km h}^{-1}

:

v_c = 82.5 \times \dfrac{18}{5} \text{ km h}^{-1} = 297 \text{ km h}^{-1}

A traffic policeman blows a whistle to halt an approaching...

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