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. 44687
• D. 44871

Answer 1

Answer: (B)

2

Answer 2

Using the formula $f'=f \bigg(\frac{v+v_0}{v}\bigg)$
we get, \hspace23mm 5.5=5 \bigg(\frac{v+v_A}{v}\bigg)\hspace20mm...(i)
and \hspace25mm 6.0=5 \bigg(\frac{v+v_B}{v}\bigg)\hspace25mm...(ii)
Here, \hspace10mm v = speed of sound
\hspace20mm v_A = speed of train A
\hspace20mm v_B = speed of train B
Solving Eqs. (i) and (ii), we get $\frac{v_B}{v_A}=2$