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 . what is the ration of velocity of train B to that of train A ?

Explanation

Let , ` u_(A) ` be the velocity of train A .
` therefore ` Frequency of siren relative to the passenger of train A ,
` n_(1) = n((V + u_(A))/(V))`
` therefore ` 5((V _ u_(A))/(V)) = 5.5 ` …(1)
Similarly , frequency of siren relative to the passenger of train B .
` n_(2) = n((V + u_(B))/(V)) [ u_(B) ` = velocity of train B]
` therefore 5 ((V + u_(g))/(V))= 6 ` ...(2)
From equation (1) , 5.5V -5V = 5u_(A) `
therefore V = (5)/(0.5 )u_(A)` ...(3)
` From equation (2) . 6V - 5V = 5u_(g)`
` therefore V = 5u_(g)` ...(4)
Comparing equation (3) and (4) , ` (5)/(0.5) u_(A) = 5u_(g)`
` (u_(B))/(u_(A)) = (1)/(0.5) = 2/1 therefore u_(B) : u_(A) = 2: 1 ` .