Question:medium
A pipe open at both ends has a fundamental frequency \(f\) in air. The pipe is now dipped vertically in water drum to half of its length. The fundamental frequency of the air column is now equal to:
A pipe open at both ends has a fundamental frequency \(f\) in air. The pipe is now dipped vertically in water drum to half of its length. The fundamental frequency of the air column is now equal to:
Show Hint
Remember the fundamental frequencies for open and closed pipes. For an open pipe of length \(L\), \(f = v/(2L)\). For a closed pipe of length \(L\), \(f = v/(4L)\). When an open pipe is half-submerged, it effectively becomes a closed pipe of half the original length.
Updated On: Nov 26, 2025
- \( f \)
- \( \frac{3}{4} f \)
- \( 2f \)
- \( \frac{1}{2} f \)
Hide Solution
The Correct Option is A
Solution and Explanation
A pipe open at both ends has a fundamental frequency \( f \) in air, calculated as \( f = \frac{v}{2L} \), where \( v \) is the speed of sound and \( L \) is the pipe length.
When submerged in water to half its length, the pipe functions as a closed pipe with an effective length of \( \frac{L}{2} \).
The fundamental frequency \( f' \) for a closed pipe is \( f' = \frac{v}{4L'} \).
Substituting \( L' = \frac{L}{2} \) yields \( f' = \frac{v}{4 \times \frac{L}{2}} = \frac{v}{2L} \), which equals the original frequency \( f \).
Consequently, the fundamental frequency remains \( f \) when the pipe is dipped to half its length in water.
The correct answer is \( f \).
Was this answer helpful?
2