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A train is moving on a straight track with a speed of 20 m s⁻¹. It is blowing its whistle at the frequency of 1000 Hz. The percentage change in frequency heard by a person standing near the track as the train passes him is (speed of sound = 320 m s⁻¹) close to:

1. 18%
2. 24%
3. 6%
4. 12%

Correct answer: 12%

Solution

The percentage change in frequency is calculated using the Doppler effect formula, which accounts for the relative motion between the source of sound (the train) and the observer. As the train approaches, the frequency increases, and as it moves away, it decreases, leading to a net change that can be expressed as a percentage of the original frequency, resulting in a 12% change.

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