Question

A train has just completed U-curve in a track which is a semi-circle. 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 200Hz.Velocity of sound is 340 m/sec.Then the apparent frequency as observed by a passenger in the middle of the train, when the speed of the train is 30 m/sec is

• A. 181 Hz
• B. 200 Hz
• C. 188 Hz
• D. 210 Hz

Answer 1

The correct option is B 200 Hz

The source of whistle is at the edge of the semicircular track and the observer is half between it and diametrically opposite side. Thus they form a quadrant of a circle.
The relative velocity between the source and observer along the line joining them is zero with each having a velocity $=vcos{45}^{\circ }$

Using Doppler's Effect,

$f^{\prime }=f\left(\frac{340+30cos{45}^{\circ }}{340+30cos{45}^{\circ }}\right)=f=200Hz$