Node-to-antinode distance in standing waves

Steps:

• In a standing wave, nodes are points of zero displacement and antinodes are points of maximum displacement.
• The pattern repeats every half wavelength, with a node and antinode spaced λ/4 apart.
• Given that the distance between a node and adjacent antinode is L, this equals λ/4.
• Thus, λ = 4L.

Why D is correct:

• By definition, the node-to-antinode interval in a standing sound wave is one-quarter wavelength (λ/4), so λ = 4L.

Why the others are wrong:

• A: ½L confuses the full node-to-node distance (λ/2) with node-to-antinode.
• B: L assumes the interval is the full wavelength, ignoring the quarter-wave segment.
• C: 2L mistakes the interval for half a wavelength, which is node-to-node.

Final answer: D