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
IIT 2002, Diffcult
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(b) In both the cases observer is moving towards, the source.
Hence by using $n' = n\left( {\frac{{v + {v_0}}}{v}} \right)$
When passenger is sitting in train $A$, then
$5.5 = 5\left( {\frac{{v + {v_A}}}{v}} \right)$ …$(i)$
when passenger is sitting in train $B$, then
$6 = 5\left( {\frac{{v + {v_B}}}{v}} \right)$ …$(ii)$
On solving equation $(i)$ and $(ii)$ we get $\frac{{{v_B}}}{{{v_A}}} = 2$
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