question_answer

A car sounding a horn of frequency 1000 Hz passes an observer. The ratio of frequencies of the horn noted by the observer before and after passing of the car is 11 : 9. If the speed of sound is v, the speed of the car is  [MP PET 2002]

A)            \[\frac{1}{10}v\]                 

B)            \[\frac{1}{2}v\]

C)            \[\frac{1}{5}v\]                   

D)            v

Correct Answer: A

Solution :

           \[{{n}_{Before}}=\frac{v}{v-{{v}_{c}}}n\] and \[{{n}_{After}}=\frac{v}{v+{{v}_{c}}}.n\]                                 \[\frac{{{n}_{Before}}}{{{n}_{After}}}=\frac{11}{9}=\left( \frac{v+{{v}_{c}}}{v-{{v}_{c}}} \right)\] Þ \[{{v}_{c}}\Rightarrow \frac{v}{10}\]