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AP Physics 2
14.6 Wave Interference and Standing Waves
AdvancedMCQMathematicalConceptual14.4k
A schematic diagram showing two identical vertical cylindrical tubes open at the top and partially filled with water at the bottom. The left tube has an air column of length L1 above the water level, representing the fundamental mode with a displacement node at the water surface and an antinode at height Delta L above the top rim. The right tube has a shorter water column leaving a longer air column of length L2, representing the second resonant mode with a node at the water surface and an antinode at height Delta L above the top rim. Labels L1, L2, and Delta L are clearly marked. No other labels, lines, text, or axes appear.
Resonance tube standing wave modes including end correction.
A student uses a tuning fork of known frequency \(f\) to excite standing sound waves in a cylindrical tube open at the top and closed at the bottom by water. Due to boundary effects at the open top, a displacement antinode forms at a distance \(\Delta L\) above the top opening of the tube. The student measures an air column length \(L_1\) for the fundamental resonance and a length \(L_2\) for the next higher resonance. Which of the following expressions correctly gives the speed of sound \(v\) in air and the end correction \(\Delta L\)?

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