Question

A train has just completed a U-curve in a track which is a semicircle. 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 Hz. Velocity of sound is 340 m/sec. Then the apparent frequency as observed by a passenger in the middle of a train when the speed of the train is 30 m/sec is

• A. 209 Hz
• B. 288 Hz
• C. 200 Hz
• D. 181 Hz

Answer 1

The correct option is C 200 Hz

$V_s=-30cos{45}^{0}m/s=\frac{-30}{\sqrt{2}}m/s$

$V_0=-30cos{45}^{0}m/s=\frac{-30}{\sqrt{2}}m/s$

$V=340m/s$
$\delta =200Hz$

By doppler's effect formula:
${\vartheta }^1=\vartheta \left(\frac{V-V_0}{V-V_s}\right)$

$=200\left(\frac{340-\left(\frac{-30}{\sqrt{2}}\right)}{340-\left(\frac{-30}{\sqrt{2}}\right)}\right)$

$=200Hz$