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Frequency of the echo detected by the driver of the train is (According to Doppler effect in sound) f'' = (v + u) / (v - u) × f, where f = original frequency of source of sound, f'' = apparent frequency of source because of the relative motion between source and observer. Calculate f'' when v = 330 m/s, u = 220 m/s, and f = 1000 Hz.

1. 103 Hz
2. 1412 Hz
3. 5000 Hz
4. 720 Hz

Correct answer: 1412 Hz

Solution

Using the Doppler effect formula f'' = (v + u) / (v - u) × f, substitute v = 330 m/s, u = 220 m/s, and f = 1000 Hz. This gives f'' = (330 + 220) / (330 - 220) × 1000 = 550 / 110 × 1000 = 1412 Hz.

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