A car sounding a horn of frequency \(1000 \mathrm{~Hz}\) passes a stationary observer. The ratio of frequencies of the horn noted by the observer before and after passing the car is \(11: 9\). If the speed of sound is ' \(v\) ', the speed of the car is

Frequency of a source moving towards a stationary listener is \(\mathrm{n}_{\mathrm{b}}=\left(\frac{\mathrm{v}}{\mathrm{v}-\mathrm{v}_{\mathrm{s}}}\right) \mathrm{n}\)
Frequency of a source moving towards a stationary listener is \(\mathrm{n}_{\mathrm{a}}=\left(\frac{\mathrm{v}}{\mathrm{v}+\mathrm{v}_{\mathrm{s}}}\right) \mathrm{n}\)
Taking the ratio
\(
\frac{\mathrm{n}_{\mathrm{b}}}{\mathrm{n}_{\mathrm{a}}}=\left(\frac{\mathrm{v}+\mathrm{v}_{\mathrm{s}}}{\mathrm{v}-\mathrm{v}_{\mathrm{s}}}\right)
\)
\(\begin{aligned} & \frac{11}{9}=\left(\frac{\mathrm{v}+\mathrm{v}_{\mathrm{s}}}{\mathrm{v}-\mathrm{v}_{\mathrm{s}}}\right) \\ & 11 \mathrm{v}+11 \mathrm{v}_{\mathrm{s}}=9 \mathrm{v}-9 \mathrm{v}_{\mathrm{s}} \\ & 2 \mathrm{v}=20 \mathrm{v}_{\mathrm{s}} \\ & \mathrm{v}_{\mathrm{s}}=\frac{1}{10} \mathrm{v}\end{aligned}\)