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The fundamental frequency in an open organ pipe is equal to the third harmonic of a closed organ pipe. If the length of the closed organ pipe is 20 cm, the length of the open organ pipe is

1. 13.2 cm
2. 8 cm
3. 16 cm
4. 12.5 cm

Correct answer: 12.5 cm

Solution

The fundamental frequency of an open organ pipe is given by v/2L, and the third harmonic of a closed organ pipe is given by 3v/4L. Equating these and substituting L (length of the closed pipe) as 20 cm, we get the length of the open pipe as 12.5 cm.

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