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AP Physics 2 · Question of the Day

AP Physics 2 Question of the Day

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Monday, September 21, 2026

A string fixed at both ends vibrates in its second harmonic, producing nodes at both ends and one additional node at the center. Which location is an antinode?

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Question of the Day

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A string fixed at both ends vibrates in its second harmonic, producing nodes at both ends and one additional node at the center. Which location is an antinode?

  1. At x=L4x=\tfrac{L}{4} (one-quarter of the length from an end). (correct answer)
  2. At x=L2x=\tfrac{L}{2} (the center).
  3. At x=0x=0 (the left end).
  4. At x=Lx=L (the right end).

Explanation: This question tests understanding of wave interference and standing waves. The second harmonic on a string fixed at both ends has nodes at x = 0, L/2, and L, with antinodes at x = L/4 and 3L/4. Since the string contains exactly one full wavelength (two half-wavelengths), the antinode positions are at one-quarter and three-quarters of the length. Choice C incorrectly identifies the center as an antinode, but x = L/2 is actually a node in the second harmonic. Choice A and D are always nodes for any harmonic on a fixed-fixed string. To find antinode positions, remember they occur midway between adjacent nodes, at odd multiples of L/4 for the second harmonic.