A train has just complicated a U-curve in a track which is a semi… - Vidyadip

MCQ

A train has just complicated 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 semicircular track. The driver blows a whistle of frequency $200 \mathrm{~Hz}$. Velocity of sound is $340 \mathrm{~m} / \mathrm{sec}$. Then the apparent frequency as observed by a passenger in the middle of a train when the speed of the train is $30 \mathrm{~m} / \mathrm{sec}$ is

A
$209 \mathrm{~Hz}$
B
$288 \mathrm{~Hz}$
✓
$200 \mathrm{~Hz}$
D
$181 \mathrm{~Hz}$

✓

Answer

Correct option: C.

$200 \mathrm{~Hz}$

The situation is shown in the fig.
Both the source (engine) and the observer (Person in the middle of the train) have the same speed, but their direction of motion is right angles to each other. The component of velocity of observer towards source is $v \cos 45^{\circ}$ and that of source along the time joining the observer and source is also $v \cos 45^{\circ}$. There is number relative motion between them, so there is no change in frequency heard. So frequency heard is $200 \ Hz .$

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