question_answer

A racing car moving towards a cliff, sounds its horn. The driver observes that the sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If \[v\] is the velocity of sound, then the velocity of the car is [KCET 2002; CBSE PMT 2004]

A)            \[v/\sqrt{2}\]                       

B)            \[v/2\]

C)            \[v/3\]                                    

D)            \[v/4\]

Correct Answer: C

Solution :

           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, \[2n=n\left( \frac{v+{{v}_{car}}}{v-{{v}_{car}}} \right)\] Þ \[{{v}_{car}}=v/3.\]