Standing wave nodes in closed tube

Steps:

• Dust heaps form at nodes of the standing wave inside the closed tube.
• Four heaps span three node intervals, so distance between consecutive nodes is 30 cm / 3 = 10 cm = 0.1 m.
• Node separation equals λ/2, so λ = 2 × 0.1 m = 0.2 m.
• Frequency f = v / λ = 330 m/s / 0.2 m = 1650 Hz.

Why A is correct:

• Matches f = v / λ for λ derived from node spacing in a standing wave.

Why the others are wrong:

• B: Assumes λ = 0.15 m (two intervals), ignoring three node gaps.
• C: Assumes λ = 0.1 m (full wavelength over 30 cm), confusing node vs. antinode spacing.
• D: Assumes λ = 0.05 m (six intervals), doubling the node count error.

Final answer: A