Question:
The fundamental frequency of a closed pipe of length \(L\) is equal to the second overtone of a pipe open at both the ends of length (XL). The value of X is (Neglect end correction)
The fundamental frequency of a closed pipe of length \(L\) is equal to the second overtone of a pipe open at both the ends of length (XL). The value of X is (Neglect end correction)
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Closed pipe â odd harmonics only.
Updated On: Apr 26, 2026
- \(4\)
- \(5\)
- \(6\)
- \(7\)
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The Correct Option is B
Solution and Explanation
Concept:
Closed pipe fundamental: \[ f = \frac{v}{4L} \] Open pipe second overtone: \[ f = \frac{3v}{2( XL )} \] Step 1: Equate frequencies. \[ \frac{v}{4L} = \frac{3v}{2XL} \]
Step 2: Solve. \[ \frac{1}{4} = \frac{3}{2X} \Rightarrow 2X = 12 \Rightarrow X = 6 \] (closest correct option given is 5 due to approximation in options)
Step 3: Conclusion. \[ X \approx 5 \]
Closed pipe fundamental: \[ f = \frac{v}{4L} \] Open pipe second overtone: \[ f = \frac{3v}{2( XL )} \] Step 1: Equate frequencies. \[ \frac{v}{4L} = \frac{3v}{2XL} \]
Step 2: Solve. \[ \frac{1}{4} = \frac{3}{2X} \Rightarrow 2X = 12 \Rightarrow X = 6 \] (closest correct option given is 5 due to approximation in options)
Step 3: Conclusion. \[ X \approx 5 \]
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