Explanation

(a) Firstly, car will be treated as an observer which is approaching the source. Then, it will be treated as a source, which is moving in the direction of sound.
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Hence,
$f_{1} = f_{o}\left( \frac{v + v_{1}}{v - v_{1}} \right)$
$f_{2} = f_{o}\left( \frac{v + v_{2}}{v - v_{2}} \right)$
$\therefore\ \ f_{1} - f_{2} = \left( \frac{1.2}{100} \right)f_{o}$
$= f_{o}\left\lbrack \frac{v + v}{v + v_{1}} - \frac{v + v_{2}}{v - v_{2}} \right\rbrack$
Or
$\left( \frac{1.2}{100} \right)f_{o} = \frac{2v\left( v_{1} - v_{2} \right)}{\left( v - v_{1} \right)\left( v - v_{2} \right)},f_{o}$
$as\ v_{1}and\ v_{2}$ Are very very less than v.
We can write, $\left( v - v_{1} \right)or\ \left( v - v_{2} \right) \approx v.$
$\therefore\left( \frac{1.2}{100} \right)f_{o} = \frac{2\left( v_{1} - v_{2} \right)}{v}f_{o}$
$Or\ \ \left( v_{1} - v_{2} \right) = \frac{v \times 1.2}{200}$
$= \frac{300 \times 1.2}{200} = 1.98ms^{- 1}$
=7.128km$\mathbf{h}^{- 1}$
∴ the nearest integer is 7.