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 200 Hz. 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
Answers
Option B is Correct
Answer:
B) 200hz
Explanation:
Frequency of whistle = 200Hz (Given)
Velocity of sound = 340 m/sec (Given)
Both the source (engine) and the observer (Person in the middle of the train) are having the same speed, but their direction of motion is at right angle to each other. The source of whistle will be at the edge of the semicircular track and the observer is half between. Thus a quadrant of circle will be formed. The component of velocity of observer towards source is vcos45 and that of source along the time joining the observer and source is also vcos45
As per the doppler effect -
f' = f (340+30cos45°/ 340+30cos45°)
f = 200hz
There is number relative motion between both, thus there will be no change in frequency heard. So the frequency heard is 200 Hz.