A wave traveling in one direction on the string reflects off the end, and returns inverted because the end is fixed. This gives two identical waves traveling in opposite directions on the string, just what is needed for a standing wave.

Although this point is not illustrated in the simulation, to build up a large standing wave on the string you must account for the reflections that occur at both ends of the string. Constructive interference takes place for all reflected waves simultaneously only when the wavelength is related to the length L of the string by:

nλ/2 = L, where n = 1, 2, 3, ...

Using f = v/λ the corresponding frequencies are:

f = nv/2L, where n = 1, 2, 3, ...

A large-amplitude standing wave builds up because of resonance for these special frequencies only. Note that there is always a node at a fixed end.

The lowest resonance frequency (n=1) is known as the fundamental frequency for the string. All the higher frequencies are known as harmonics - these are integer multiples of the fundamental frequency.

All stringed musical intruments have strings fixed at both ends. When they are played the sound you hear is some combination of the fundamental frequency and the different harmonics - it's because the harmonics are included that the sound sounds musical. A pure sine wave does not sound nearly so nice.