Standing wave nodes in closed tube separated by λ/2

Steps:

• Calculate wavelength: λ = v / f = 340 m/s / 2000 Hz = 0.17 m = 17 cm.
• Distance between consecutive nodes: λ/2 = 17 cm / 2 = 8.5 cm.
• In the diagram, x spans 5 intervals between 6 nodes (from closed end node to the fifth inner node).
• Thus, x = 5 × 8.5 cm = 42.5 cm ≈ 42 cm.

Why B is correct:

• Matches x = 5(λ/2), as nodes form at multiples of λ/2 from the closed end in a closed tube standing wave.

Why the others are wrong:

• A: Matches ≈3(λ/2) = 25.5 cm or 7λ/4 ≈ 30 cm (third harmonic length), but diagram implies more intervals.
• C: Matches ≈7(λ/2) = 59.5 cm or 15λ/4 ≈ 64 cm (higher harmonic length), exceeding diagram's node count.
• D: Matches ≈13(λ/2) = 110.5 cm, unrelated to odd-quarter multiples for closed tube.

Final answer: B