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AP Physics 2
14.6 Wave Interference and Standing Waves
IntermediateMCQMathematicalConceptual15.1k
Two horizontal cylindrical pipes are shown one above the other. The upper pipe, labeled Pipe 1, has two horizontal parallel line segments representing its walls, with both the left and right ends open. The lower pipe, labeled Pipe 2, has the same length and diameter, with its left end open and its right end closed by a thick vertical line segment. Below each pipe is a horizontal double-headed dimension arrow labeled \(L\). No wave patterns, nodes, antinodes, or curves appear inside either pipe. No other labels, lines, text, or axes appear.
Pipe 1 is open at both ends; Pipe 2 is open at one end and closed at the other.
Two identical cylindrical pipes, each of length \(L\), are filled with air. Pipe 1 is open at both ends and vibrates in its fundamental mode at frequency \(f_1\). Pipe 2 is open at one end and closed at the other end. Which row in the table correctly identifies the fundamental frequency of Pipe 2 in terms of \(f_1\), the harmonics allowed in Pipe 2, and the ratio of the frequency of the second resonant standing wave mode in Pipe 2 to its fundamental frequency?

Fundamental Frequency of Pipe 2Allowed Harmonics in Pipe 2Ratio of 2nd Resonant Mode Frequency to 1st Resonant Mode Frequency
(A)\(2f_1\)All integer harmonics (\(n = 1, 2, 3, \dots\))\(2\)
(B)\(\dfrac{1}{2}f_1\)Odd integer harmonics only (\(n = 1, 3, 5, \dots\))\(3\)
(C)\(\dfrac{1}{2}f_1\)All integer harmonics (\(n = 1, 2, 3, \dots\))\(2\)
(D)\(2f_1\)Odd integer harmonics only (\(n = 1, 3, 5, \dots\))\(3\)

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