A wave reflected from a fixed end superposes on the incoming wave to give a standing wave y = 2A sin(kx) cos(ωt): the pattern no longer travels. The red points that never move are nodes; the points midway that swing hardest are antinodes. A string clamped at both ends only allows the modes that fit a whole number of half-wavelengths, νₙ = n·v/2L. Step the harmonic number n.
The string is clamped at both ends (blue posts); a wave and its reflection overlap.