Standing Waves on a String — two identical waves travelling in opposite directions superpose: y = A·sin(kx−ωt) + A·sin(kx+ωt) = 2A·sin(kx)·cos(ωt). The spatial part sin(kx) never moves — only the amplitude envelope pulses in time via cos(ωt). Nodes stay at zero displacement; antinodes swing between the dashed envelope.