Question:
An organ pipe closed at one end produces \(5^{\text{th}}\) overtone of an air column. It is found that air in the pipe is vibrating with \(x\) nodes and \(y\) antinodes. The value of \(x\) and \(y\) is
An organ pipe closed at one end produces \(5^{\text{th}}\) overtone of an air column. It is found that air in the pipe is vibrating with \(x\) nodes and \(y\) antinodes. The value of \(x\) and \(y\) is
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A closed pipe has a node at the closed end; each higher overtone adds one node and one antinode.
Updated On: Nov 12, 2026
- \(x=5\) and \(y=6\)
- \(x=6\) and \(y=6\)
- \(x=6\) and \(y=5\)
- \(x=5\) and \(y=5\)
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept
In a pipe closed at one end, the closed end is a node and the open end is an antinode. Only odd harmonics are present.
Step 2: Count for the overtone
The fundamental has 1 node and 1 antinode. Each next overtone adds one node and one antinode.
The 5th overtone is the 11th harmonic (frequency \(11f_1\)), so it has \(1+5=6\) nodes and \(1+5=6\) antinodes.
Step 3: Conclusion
So \(x=6\) and \(y=6\).
Final Answer:
The air column has 6 nodes and 6 antinodes. \[ \boxed{\text{(B) }x=6\text{ and }y=6} \]
In a pipe closed at one end, the closed end is a node and the open end is an antinode. Only odd harmonics are present.
Step 2: Count for the overtone
The fundamental has 1 node and 1 antinode. Each next overtone adds one node and one antinode.
The 5th overtone is the 11th harmonic (frequency \(11f_1\)), so it has \(1+5=6\) nodes and \(1+5=6\) antinodes.
Step 3: Conclusion
So \(x=6\) and \(y=6\).
Final Answer:
The air column has 6 nodes and 6 antinodes. \[ \boxed{\text{(B) }x=6\text{ and }y=6} \]
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