Question:
A pipe closed at one end vibrating in fifth overtone is in unison with open pipe vibrating in its fifth overtone. The ratio of \(l_c : l_o\) is [\(l_c = \text{vibrating length of closed pipe}, l_o = \text{vibrating length of open pipe}\)]
A pipe closed at one end vibrating in fifth overtone is in unison with open pipe vibrating in its fifth overtone. The ratio of \(l_c : l_o\) is [\(l_c = \text{vibrating length of closed pipe}, l_o = \text{vibrating length of open pipe}\)]
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Closed pipe:
Only odd harmonics
Updated On: May 8, 2026
- 12 : 11
- 1 : 1
- 11 : 12
- 5 : 1
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Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Concept:
• Closed pipe frequencies: odd harmonics
• Open pipe frequencies: all harmonics
Step 1: Fifth overtone.
• Closed pipe: 6th harmonic not allowed → 11th harmonic \[ f_c = \frac{11v}{4l_c} \]
• Open pipe: 6th harmonic \[ f_o = \frac{6v}{2l_o} = \frac{3v}{l_o} \]
Step 2: Equate frequencies. \[ \frac{11v}{4l_c} = \frac{3v}{l_o} \]
Step 3: Solve. \[ \frac{l_c}{l_o} = \frac{11}{12} \]
Step 4: Conclusion.
Ratio = $11:12$ Final Answer: Option (C)
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