Question

A siren placed at a railway platform is emitting sound of frequency $5kHz$. A passenger sitting in a moving train A records a frequency of $5.5kHz$ while the train approaches the siren. During his return journey in a different train $B$ he records a frequency of $6.0kHz$ while approaches the same siren. The ratio of the velocity of train $B$ to that train $A$ is

• A. $242/252$
• B. $2$
• C. $5/6$
• D. $11/6$

Answer 1

Answer: (B)

$2$

Frequency of siren, $n=5kHz$

Let velocity of train A $=v_A$

Let velocity of train B $=v_B$

Frequency of sound of train A recorded by observer $=n_{OA}=5.5kHz$

Frequency of sound of train B recorded by observer $=n_{OB}=6kHz$

For train A;

$\frac{5.5}{5}=\frac{v_A+v}{v}$

$\Rightarrow 5.5v=5v_A+5v$

$\Rightarrow 0.5v=5v_A$

$\Rightarrow v=10v_A$ ..................(1)

For train B;

$\frac{6}{5}=\frac{v_B+v}{v}$

$\Rightarrow v=5v_B$ ..................(2)

From (1) and (2);

$\frac{v_B}{v_A}=2$