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

D

Explanation

`f_(approach)_(A)=5.5kHz=((v+v_A)/(v))5` ..(i)
`f_(approach)_(B)=6kHz=((v+v_B)/(v))5` ..(ii)
Where `v` is the velocity of sound. Now,
`5.5=(1+(v_A)/(v))5`
`implies(v_A)/(v)=0.1` .(iii)
similarly, `6=(1+(v_B)/(v))5`
`implies(v_B)/(v)=0.2` .(iv)
`implies(v_B)/(v_A)=2`