standing wave
Pluck a guitar string and, though waves race back and forth along it, the overall shape just sits there vibrating in place, some points never move while others swing wildly. That frozen-looking, vibrating pattern is a standing wave. The question it answers is: what happens when a wave reflects and meets itself coming back?
A standing wave forms when two waves of the same frequency and amplitude travel in opposite directions and superpose, typically a wave and its own reflection from a fixed end. Their superposition produces a pattern that does not travel: fixed points of zero motion called nodes, and points of maximum swing called antinodes, alternating along the medium. Neighbouring nodes are half a wavelength apart. Unlike a travelling wave, a pure standing wave transports no net energy along the medium.
Standing waves are why strings and air columns have definite musical notes: only wavelengths that fit the boundaries neatly (a whole number of half-wavelengths on a string fixed at both ends) survive. This is deeply tied to resonance. An honest note: the pattern looks stationary, but the medium is very much moving, the antinodes oscillate hard, only the nodes are still.
On a string of length L fixed at both ends, the simplest standing wave has a node at each end and one antinode in the middle, fitting exactly half a wavelength: lambda = 2L. This is the string's fundamental note.
Two opposite-going waves superpose into a fixed pattern of still nodes and swinging antinodes.
A standing wave is made of two travelling waves. The pattern stays put and, unlike a travelling wave, carries no net energy along the medium.