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In a resonance column experiment, a long tube open at the top is held vertically. Water inside can be raised or lowered. The air column from the open top to the water surface acts as a closed organ pipe. A vibrating tuning fork is held above the open end. The first resonance occurs when the water level is 24.1 cm below the open end, and the second resonance occurs when the water level is 74.1 cm below the open end. Find the diameter (in cm) of the tube.

1. 1.0
2. 1.2
3. 1.4
4. 1.6

Correct answer: 1.0

Solution

End correction e = 0.3d for a cylindrical pipe open at one end. First resonance: L1 + e = lambda/4. Second resonance: L2 + e = 3*lambda/4. The difference gives lambda, and substituting back gives e and hence d.

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