Particle motions for waves on a string

Waves on a string are transverse waves in which (to a first approximation) elements of the string oscillate in a direction perpendicular to the direction of wave motion.

In a travelling wave (below) all of the string elements have the same motion amplitude, but adjacent elements are out of phase and this creates the illusion of motion along the string.

In a standing wave (below) the string elements also oscillate in a direction perpendicular to the undisturbed string. However, the amplitude of the motion now varies along the string and some elements do not move at all.