Question

Two trains move towards each other with the same speed. Speed of sound is $340{\text{ms}}^{-1}$. If the pitch of the tone of the whistle of one when heard on the other changes by $\frac{9}{8}$ times, then the speed of each train is:

• A. $2{\text{ms}}^{-1}$
• B. $40{\text{ms}}^{-1}$
• C. $20{\text{ms}}^{-1}$
• D. $100{\text{ms}}^{-1}$

Answer 1

The correct option is C $20{\text{ms}}^{-1}$

$f^{\prime }=\frac{9}{8}f{f}^{\prime }=\left(\frac{c+v_0}{c-v_s}\right)f(\because v_s=v_0)$
$\frac{f^{\prime }}{f}=\frac{c+v_0}{c-v_0}$
put the values here
$\Rightarrow \frac{9}{8}=\frac{c+v_0}{c-v_0}$
$\frac{9}{8}=\frac{340+v}{340-v}$
$9\times 340-9v=8\times 340+8v$
$17v=340\times 1$
$v=\frac{340}{17}=20\text{m/sec}$