Question:
A cylindrical tube open at both the ends has a fundamental frequency of 390 Hz in air. If 1/4th of the tube is immersed vertically in water the fundamental frequency of air column is
A cylindrical tube open at both the ends has a fundamental frequency of 390 Hz in air. If 1/4th of the tube is immersed vertically in water the fundamental frequency of air column is
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Immersing an open tube turns it into a closed organ pipe.
Updated On: Apr 10, 2026
- 260 Hz
- 130 Hz
- 390 Hz
- 520 Hz
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The Correct Option is A
Solution and Explanation
Step 1: Open Tube
Fundamental frequency $n = \frac{v}{2L} = 390~\text{Hz}$.
Step 2: Closed Tube Formation
Immersion turns it into a closed tube. Remaining air length $L' = \frac{3}{4}L$.
Step 3: New Frequency
New fundamental frequency $n' = \frac{v}{4L'} = \frac{v}{4(3L/4)} = \frac{v}{3L} = \frac{2}{3}(\frac{v}{2L})$.
$n' = \frac{2}{3} \times 390 = 260~\text{Hz}$.
Final Answer: (a)
Fundamental frequency $n = \frac{v}{2L} = 390~\text{Hz}$.
Step 2: Closed Tube Formation
Immersion turns it into a closed tube. Remaining air length $L' = \frac{3}{4}L$.
Step 3: New Frequency
New fundamental frequency $n' = \frac{v}{4L'} = \frac{v}{4(3L/4)} = \frac{v}{3L} = \frac{2}{3}(\frac{v}{2L})$.
$n' = \frac{2}{3} \times 390 = 260~\text{Hz}$.
Final Answer: (a)
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