Question

A train moving at a speed of $30\text{m/s}$ has just completed a U-curve in a semi-circular track. The engine is at the forward end of the semi-circular part of the track while the last carriage is at the rear end of the semi-circular track. The driver blows a whistle of frequency $200\text{Hz}$. If the velocity of sound is $340\text{m/s}$, then the apparent frequency as observed by a passenger in the middle of the train is

• A. $219\text{Hz}$
• B. $188\text{Hz}$
• C. $200\text{Hz}$
• D. $181\text{Hz}$

Answer 1

The correct option is C $200\text{Hz}$


$f_{app}=f_0\left(\frac{v\pm v_0}{v\pm v_s}\right)$

$V_0=\frac{30}{\sqrt{2}}m/s$

$V_s=\frac{30}{\sqrt{2}}m/s$

$v=340m/s$

$f_{app}=f_0\left(\frac{v+v_0}{v+v_s}\right)$

$f_{app}=200\left(\frac{340+30/\sqrt{2}}{340+30/\sqrt{2}}\right)=200Hz$