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An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is

1. 66.7 cm
2. 100 cm
3. 150 cm
4. 200 cm

Correct answer: 150 cm

Solution

For a closed organ pipe, resonance occurs at odd multiples of the quarter wavelength. The smallest length corresponds to λ/4, so the next resonance occurs at 3λ/4. If the first length is 50 cm, the next length is 3 × 50 = 150 cm.

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