nodes

Meaning: A node is a point in a standing wave where the medium stays at zero displacement at all times, because the two oppositely traveling waves (incident and reflected) always interfere destructively there. Antinodes, where amplitude is maximum, lie midway between nodes, and adjacent nodes are λ/2 apart. A fixed end of a string is a node. (In biology, a node of Ranvier is a gap in an axon's myelin sheath.)

Equation: L = nλ/2, where L is the string length (m), λ is the wavelength (m), and n = 1, 2, 3… is the harmonic number (dimensionless). A string fixed at both ends has n + 1 nodes, counting the ends.

On the MCAT: Passages show a string or pipe vibrating at a harmonic. You count nodes, find λ, or compare frequencies using fn = nv/2L. A pipe closed at one end has a displacement node at the closed end and an antinode at the open end, so only odd harmonics occur (L = nλ/4, n odd).

Common confusion: Students put nodes at the open end of a pipe. Open ends are displacement antinodes (they are pressure nodes), so define a node by zero displacement, not by the end of the pipe.