When a car is approaching the observer, the frequency of horn is...

Apparent frequency when source of moving towards observer, ${f}_{1} = 100 = {f}_{0}\left(\dfrac{c}{c - {v}_{s}}\right) . . . \left(1\right)</p><p>Here,${f}_{0} =$frequency of observer,$c =$speed of sound and${v}_{s} =$speed of source.</p><p>Apparent frequency when source of moving away from observer, </p><p>${f}_{2} = 50 = {f}_{0}$\left(\dfrac{c}{c + {v}_{s}}\right)$ . . . \left(2\right)$</p><p>From above two equations, we have </p><p>$\dfrac{{f}_{1}}{{f}_{2}} = 2 = \dfrac{c + {v}_{s}}{c - {v}_{s}}$</p><p>$⇒ 2c - 2{v}_{s} = c + {v}_{s}$</p><p>$⇒ 3{v}_{s} = c$</p><p>Putting the value in equation \left(1\right)$, we have

$100 = {f}_{0}\dfrac{c}{\dfrac{2c}{3}} = \dfrac{3}{2}{f}_{0}$

$⇒ {f}_{0} = \dfrac{200}{3}Hz$

Hence, $x = 200$.