antinodes

Meaning: An antinode is a point on a standing wave where the oscillation amplitude is maximum. A standing wave forms when two waves of equal frequency travel in opposite directions, often an incident wave and its reflection. At an antinode the waves are always in phase, so they interfere constructively and the amplitude is up to twice that of either wave. Nodes lie midway between neighboring antinodes, so adjacent antinodes are λ/2 apart.

Equation: f = nv/(2L), where f is the frequency of the nth harmonic (Hz), n is the harmonic number (dimensionless) and equals the number of antinodes on a string fixed at both ends, v is wave speed (m/s), and L is string length (m).

On the MCAT: Passages show a string or air column with a drawn pattern. Count loops to find the harmonic, use λ/2 spacing to find λ, then v = fλ. A pipe open at both ends has antinodes at both ends; a pipe closed at one end has a node there and an antinode at the open end, giving odd harmonics only.

Common confusion: An antinode is not a crest; it swings between +2A and −2A. For sound, a displacement antinode is a pressure node, so check which quantity is asked.