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 `5.5kHz` 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 the velocity of train `B` to that of train `A` is

Options

A. `(242)/(252)`
B. `2`
C. `(5)/(6)`
D. `(11)/(6)`

Answer

B

Explanation

Using the formula
`f' = f((v + v_(0))/(v))`
we get `5.5 = 5 ((v + v_(A))/(v))`…….(1)
and `6.0 = 5((v + v_(B))/(v))`…..(2)
here `v =` speed of sound
`v_(A) =` speed of train `A`
and `v_(B) =` speed of train `B`
solving eqn. `(1)` and `(2)` we get :
`(v_(B))/(v_(A)) = 2`