First slide

Doppler's effect

Question

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 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

Moderate

A

209 Hz
B

288 Hz
C

200 Hz
D

181 Hz

Solution

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 $v \cos 45 °$ and that of source along the time joining the observer and source is also $v \cos 45 °$ . 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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