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

`{:(rarr v_(s) = 0,, larr v_(o) = u_(A)),(overset(*)(S),overset(v)rarr,overset(*)(O)):}`
`f' = f((v+v_(0))/(v))`
`5.5=5((v+u_(A))/(v)) rArr 1.1 = (330+u_(A))/(330)`
`u_(A) = 33 m//s`
`{:(rarr v_(o) = u_(B),, larr v_(s) = 0),(overset(*)(O),overset(v)rarr,overset(*)(S)):}`
`f' = f((v+v_(0))/(v))`
`6 = 5((v+u_(B))/(v)) rArr 1.2 = (330+u_(B))/(330)`
`u_(B) = 66 m//s`
`(u_(B))/(u_(A)) = 2`