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  3. Physics
  4. 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.

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Q. 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 JEEIIT JEE 2002Waves

Solution:

Using the formula $f'=f \bigg(\frac{v+v_0}{v}\bigg)$
we get, $ 5.5=5 \bigg(\frac{v+v_A}{v}\bigg)$...(i)
and $ 6.0=5 \bigg(\frac{v+v_B}{v}\bigg)$...(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 $\frac{v_B}{v_A}=2$