question_answer

A siren placed at a railway platform is emitting sound of frequency 5 kHz. A passenger sitting in a moving train A records a frequency of 5.5 kHz while the train approaches the siren. During his return journey in a different train B he records a frequency of 6.0 kHz while approaching the same siren. The ratio of the velocity of train B to that of train A is [IIT-JEE (Screening) 2002]

A)            242/252                                  

B)            2

C)            5/6

D)            11/6

Correct Answer: B

Solution :

           In both the cases observer is moving towards, the source. Hence by using \[{n}'=n\left( \frac{v+{{v}_{0}}}{v} \right)\]                        When passenger is sitting in train A, then                             \[5.5=5\left( \frac{v+{{v}_{A}}}{v} \right)\]                    ?(i)                    when passenger is sitting in train B, then                                \[6=5\left( \frac{v+{{v}_{B}}}{v} \right)\]                    ?(ii) On solving equation (i) and (ii) we get \[\frac{{{v}_{B}}}{{{v}_{A}}}=2\]