stationary source is emitting sound at a fixed frequency $f_0$, which is reflected by two cars approaching the source. The difference between the frequencies of sound reflected from the cars is $1.2\%$ of $f_0$. What is the difference in the speeds of the cars (in $km$ per hour) to the nearest integer ..... $km/hr$ ? The cars are moving at constant speeds much smaller than the speed of sound which is $330$ $ms^{-1}$.
Diffcult
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Apparent frequency of sound reflected from car $\mathrm{f}=\left(\frac{\mathrm{v}+\mathrm{v}_{0}}{\mathrm{v}-\mathrm{v}_{0}}\right) \mathrm{f}_{0} \approx\left(1+\frac{2 \mathrm{v}_{0}}{\mathrm{v}}\right) \mathrm{f}_{0}$
$\because \frac{\Delta f}{f_{0}} \times 100=1.2 \therefore \frac{2 v_{0}}{v}=\frac{1.2}{100}$
$\Rightarrow \mathrm{v}_{0}=2 \mathrm{\,ms}^{-1}=2 \times \frac{18}{5} \mathrm{\,km} / \mathrm{h} \approx 7 \mathrm{\,km} / \mathrm{h}$
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