Question:
The fundamental frequency of a closed organ pipe of length L is equal to the frequency of the first overtone of an open organ pipe of length L'. The relation between their lengths is:
The fundamental frequency of a closed organ pipe of length L is equal to the frequency of the first overtone of an open organ pipe of length L'. The relation between their lengths is:
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Closed pipe: odd harmonics only
Open pipe: all harmonics
First overtone of open pipe = second harmonic
Updated On: Jun 10, 2026
- \( L' = 4L \)
- \( L' = 2L \)
- \( L = L' \)
- \( L' = \frac{L}{2} \)
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The Correct Option is A
Solution and Explanation
Concept:
Closed pipe (one end closed):
\[
f_c = \frac{v}{4L}
\]
Open pipe:
\[
f_1 = \frac{v}{2L'}, \quad \text{first overtone} = \frac{2v}{2L'} = \frac{v}{L'}
\]
Step 1: Equate frequencies \[ \frac{v}{4L} = \frac{v}{L'} \]
Step 2: Solve \[ L' = 4L \]
Step 1: Equate frequencies \[ \frac{v}{4L} = \frac{v}{L'} \]
Step 2: Solve \[ L' = 4L \]
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