question_answer

A car is moving towards a high cliff. The car driver sounds a horn of frequency T. The reflected sound heard by the driver has a frequency 2f. If V be the velocity of sound then the velocity of the car, in the same velocity units, will be :-

A)  \[\frac{v}{3}\]                               

B)  \[\frac{v}{4}\]

C)  \[\frac{v}{2}\]                                  

D)  \[\frac{v}{\sqrt{2}}\]

Correct Answer: A

Solution :

According to given condition cliff is stationary source of freq. f? where             \[f'=\left( \frac{v}{v-{{v}_{\infty }}} \right)\,f\] Freq. heard by the driver \[f''=\left( \frac{v+{{v}_{car}}}{v} \right)f'=\left( \frac{v+{{v}_{car}}}{v-{{v}_{car}}} \right)\,f=2f\] \[\Rightarrow \] s\[v+{{v}_{car}}=2v-2{{v}_{car}}\] \[\Rightarrow \]\[3{{v}_{car}}=v\] \[\Rightarrow \]\[{{v}_{car}}=v/3\]