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. The ratio of the velocity of train B to that of train A is.

Question

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. The ratio of the velocity of train B to that of train A is. (A) 242/252 (B) 2 (C) 5/6 (D) 11/6

Tardigrade Admin · Accepted Answer

Using the formula f'=f ((v+v0/v)) we get, 5.5=5 ((v+vA/v))...(i) and 6.0=5 ((v+vB/v))...(ii) Here, v = speed of sound vA = speed of train A vB = speed of train B Solving Eqs. (i) and (ii), we get (vB/vA)=2

242/252

2

5/6

11/6

Using the formula f′=f(vv+v0​​) we get, 5.5=5(vv+vA​​)...(i) and 6.0=5(vv+vB​​)...(ii) Here, v= speed of sound vA​= speed of train A vB​= speed of train B Solving Eqs. (i) and (ii), we get vA​vB​​=2

Using the formula $f^{'} = f (\frac{v + v _{0}}{v})$
we get, $5.5 = 5 (\frac{v + v _{A}}{v})$ ...(i)
and $6.0 = 5 (\frac{v + v _{B}}{v})$ ...(ii)
Here, $v =$ speed of sound
$v_{A} =$ speed of train A
$v_{B} =$ speed of train B
Solving Eqs. (i) and (ii), we get $\frac{v _{B}}{v _{A}} = 2$