A siren placed at a railway platform is emitting sound of frequency $5\text{ kHz}$. A passenger sitting in a…

A siren placed at a railway platform is emitting sound of frequency $5\text{ kHz}$. A passenger sitting in a moving train $A$ records a frequency of $5.5\text{ kHz}$ while train approaches the siren. During his return journey in a different train $B$, he records a frequency of $6\text{ kHz}$ while approaching the same siren. The ratio of the velocity of train $B$ to that of train $A$ is
  1. $4/3$
  2. $2$
  3. $5/3$
  4. $8/5$

Solution

When passenger is sitting in moving train $A$, $5.5 = 5 \left(\frac{v + v_A}{v}\right)$ or $\frac{v_A}{v} = \frac{1}{10}$ ...(i) When passenger is sitting in moving train $B$, $6 = 5 \left(\frac{v + v_B}{v}\right)$ or $\frac{v_B}{v} = \frac{1}{5}$ ...(ii) From Eqs. (i) and (ii), we get $\frac{v_B}{v_A} = 2$

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