A stationary source is emitting sound at a fixed frequency $\mathrm{f}_0$, 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 $\mathrm{km}$ per hour) to the nearest integer? The cars are moving at constant speeds much smaller than the speed of sound which is $330 \mathrm{~ms}^{-1}$.
IIT 2010, Advanced
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$f_{\text {app }}=f_0 \frac{c+v}{c-v}$
$\mathrm{df}=\frac{2 \mathrm{f}_0 \mathrm{c}}{(\mathrm{c}-\mathrm{v})^2} \mathrm{dv}$
where $c$ is speed of sound
$\mathrm{df}=\frac{1.2}{100} \mathrm{f}_0$
hence $d v \approx 7 \mathrm{~km} / \mathrm{hr}$.
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