A siren placed at a railway platformis 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 . what is the ration of velocity of train B to that of train A ?

A siren placed at a railway platformis emitting sound of frequency 5 K

1.	A siren placed at a railway platformis 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 . what is the ration of velocity of train B to that of train A ?
Answer» Solution :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] ` therefore5 ((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) = 2/1therefore u_(B) : u_(A) = 2: 1 ` .