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 velocity of train B to that of train A is

• A. $\frac{242}{252}$
• B. $2$
• C. $\frac{5}{6}$
• D. $\frac{11}{6}$

Answer 1

The correct option is B $2$

$(f_{approach}{)}_A=5.5kHz=\left(\frac{v+v_A}{v}\right)\mathrm{5........}(i\left)\right(f_{approach}{)}_B=6kHz=\left(\frac{v+v_B}{v}\right)\mathrm{5........}\left(ii\right)$
Where v is the velocity of sound. Now,
$5.5=(1+\frac{v_A}{v})5\Rightarrow \frac{v_A}{v}=\mathrm{0.1.........}\left(iii\right)Similarly,6=(1+\frac{v_B}{v})5\Rightarrow \frac{v_B}{v}=\mathrm{0.2........}\left(iv\right)\Rightarrow \frac{v_B}{v_A}=2$