Question:
The fundamental frequency of an open organ pipe is 300 Hz. The first overtone of this pipe has the same frequency as the first overtone of a closed organ pipe. If the speed of sound is 330 m/s, then the length of the closed organ pipe is:
The fundamental frequency of an open organ pipe is 300 Hz. The first overtone of this pipe has the same frequency as the first overtone of a closed organ pipe. If the speed of sound is 330 m/s, then the length of the closed organ pipe is:
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For organ pipes:
Open pipe first overtone = 2f,
Closed pipe first overtone = (3v)/(4L).
Updated On: Mar 18, 2026
- 41 cm
- 37 cm
- 31 cm
- 80 cm
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The Correct Option is A
Solution and Explanation
Step 1: Frequency of first overtone of open pipe. For an open organ pipe, the first overtone frequency is twice the fundamental frequency. f = 2 × 300 = 600 Hz
Step 2: Frequency of first overtone of closed pipe. For a closed pipe, first overtone frequency is: f = (3v)/(4L)
Step 3: Equating frequencies and solving. 600 = (3 × 330)/(4L) L = 0.4125 m ≈ 41 cm
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