Question:
A pipe open at both ends has a fundamental frequency \(f\) in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :
A pipe open at both ends has a fundamental frequency \(f\) in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now :
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Half the pipe in water makes an air column of length L/2, closed at the water end and open at the other.
Updated On: Nov 11, 2026
- \(2f\)
- \(f\)
- \(\frac{f}{2}\)
- \(\frac{3f}{4}\)
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The Correct Option is B
Solution and Explanation
Open pipe of length \(L\): fundamental \(f = \frac{v}{2L}\).
When half is dipped in water, the air column has length \(\frac{L}{2}\), closed at the water surface and open at the top (closed pipe).
Fundamental of a closed pipe of length \(\ell\): \(f' = \frac{v}{4\ell} = \frac{v}{4(L/2)} = \frac{v}{2L} = f\).
Answer: (2) \(f\)
When half is dipped in water, the air column has length \(\frac{L}{2}\), closed at the water surface and open at the top (closed pipe).
Fundamental of a closed pipe of length \(\ell\): \(f' = \frac{v}{4\ell} = \frac{v}{4(L/2)} = \frac{v}{2L} = f\).
Answer: (2) \(f\)
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