• # question_answer 37) A car is moving towards a high cliff. The car driver sounds a horn of frequency$f$The reflected sound heard by the driver has a frequency$2f.$ If. If r be the velocity of sound, then the velocity of the car, in the same velocity units, will be: A) $\frac{v}{\sqrt{2}}$B) $\frac{V}{3}$C) $\frac{V}{4}$D) $\frac{V}{2}$

When the sound is reflected from the cliff, it approaches the driver of the car. Therefore, the driver acts as an observer and both the source (car) and observer are moving. Hence, apparent frequency heard by the observer (driver) is given by $f'=f\left( \frac{v+{{v}_{0}}}{v-{{v}_{0}}} \right)$ (i) where v = velocity of sound, ${{v}_{0}}=$velocity of car$={{v}_{s}}$ Frequency of reflected sound heard by driver $n'=n\left( \frac{v+{{v}_{O}}}{v-{{v}_{S}}} \right)$ It is given that $n'=2n$ Hence, $2n=n\left( \frac{v+{{v}_{car}}}{v-{{v}_{car}}} \right)\Rightarrow {{v}_{car}}=v/3$