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Standing waves form when two identical waves travel in opposite directions through the same medium. The resultant $y = 2A\sin(kx)\cos(\omega t)$ is a product of a spatial function and a time function — position and time are separated, unlike in a travelling wave. Points where $\sin(kx) = 0$ are nodes (permanently at rest); points where $|\sin(kx)| = 1$ are antinodes (maximum amplitude $2A$). Consecutive nodes are$\lambda/2$apart; a node-antinode pair is$\lambda/4$ apart.

Key properties: (1) No net energy transfer — energy oscillates locally between KE (at antinodes) and PE (at nodes). (2) All particles between two consecutive nodes oscillate in phase; particles on opposite sides of a node are in antiphase. (3) Every particle (except at nodes) passes through equilibrium simultaneously. The standing wave pattern depends entirely on the boundary conditions: fixed ends produce nodes, free/open ends produce antinodes. These boundary conditions determine which harmonics are allowed, making them the starting point for all pipe and string vibration problems.$