Standing Wave on String

Standing wave: pattern formed by superposition of two equal-amplitude waves traveling in opposite directions.

y(x,t) = 2A·sin(kx)·cos(ωt) — separates space and time dependence.

Has fixed NODES (zero amplitude) and ANTINODES (max amplitude). Particles oscillate but pattern doesn't propagate.

Distance between consecutive nodes: λ/2. Same for consecutive antinodes.

Distance from node to nearest antinode: λ/4.

Found on: vibrating strings (musical instruments), open/closed pipes, microwave ovens, laser cavities.

All points between two nodes oscillate IN PHASE; on opposite sides of a node, π out of phase.

Energy transport: ZERO in a perfect standing wave (no net flow).