First slide

Doppler's effect

Question

A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from 440 Hz to 480 Hz, when it gets reflected from the wall. If the speed of sound in air is 345 m/s, then the speed of the car is:

Moderate

A

18 km/hr
B

36 km/hr
C

54 km/hr
D

24 km/hr

Solution

Frequency of $s^{1} = \frac{c}{c - u} f_{s}$
Now frequency observed by driver of the car will be = $\frac{c + u}{c} f_{s^{1}} = \frac{c + u}{c} \times \frac{c}{c - u} f_{s}$
As per given data $480 = \frac{345 + u}{345 - u} \times 440$
$\begin{array}{l} \Rightarrow 12 (345 - u) = 11 (345 + u) \\ \Rightarrow 23 u = 345 \\ \Rightarrow u = \frac{345}{23} m / s \\ ∴ u = \frac{345}{23} \times \frac{18}{5} k m p h = 54 k m p h \end{array}$

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