Question

A train has just completed a 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 200 Hz. Velocity of sound is 340 m/s. Then the apparent frequency as observed by a passenger in the middle of the train, when the speed of the train is 30 m/s, is

• A. 219 Hz
• B. 188 Hz
• C. 200 Hz
• D. 181 Hz

Answer 1

The correct option is C 200 Hz

The Doppler formula holds for non-collinear motion if v_s and v₀ are taken to be the resolved component along the line of slight, In this case, we have

$v_0=-v_{t}sin{45}^{\circ }=-\frac{30}{\sqrt{2}}m/s$
$v_s=-v_{t}sin{45}^{\circ }=\frac{30}{\sqrt{2}}m/s$
We have, v = 340 m/s, n = 200 Hz. The apparent frequency n’ is given by
$n^{\prime }=n\left[\frac{v-v_0}{v-v_s}\right]=200\left[\frac{340+\left(\frac{30}{\sqrt{2}}\right)}{340+\left(\frac{30}{\sqrt{2}}\right)}\right]=200Hz$