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The fundamental frequency of a closed organ pipe of length 20 cm is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is

1. 100 cm
2. 120 cm
3. 140 cm
4. 80 cm

Correct answer: 120 cm

Solution

For a closed organ pipe, the fundamental frequency corresponds to a wavelength of 4 times its length. For an open organ pipe, the second overtone corresponds to 3 times the fundamental frequency, with a wavelength of 2 times its length. Equating the frequencies, the length of the open pipe is calculated as 120 cm.

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