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A speeding motorcyclist sees traffic jam ahead of him. He slows down to 36 km/hour. He finds that traffic has eased and a car moving ahead of him at 18 km/hour is honking at a frequency of 1392 Hz. If the speeds of sound is 343 m/s, the frequency of the honk as heard by him will be:

1. 1332 Hz
2. 1372 Hz
3. 1412 Hz
4. 1464 Hz

Correct answer: 1412 Hz

Solution

The Doppler effect formula for sound is used here: \( f' = f \frac{v + v_o}{v - v_s} \), where \( f \) is the source frequency, \( v \) is the speed of sound, \( v_o \) is the observer's speed, and \( v_s \) is the source's speed. Substituting \( f = 1392 \, \text{Hz}, v = 343 \, \text{m/s}, v_o = 36 \, \text{km/h} = 10 \, \text{m/s}, v_s = 18 \, \text{km/h} = 5 \, \text{m/s} \), we get \( f' = 1392 \times \frac{343 + 10}{343 - 5} \approx 1412 \, \text{Hz} \).

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