Standing (Stationary) Waves

A wave hits the fixed end and reflects, so the string carries two identical waves moving in opposite directions. Where they always cancel you get a node (no movement); where they always reinforce you get an antinode (maximum swing). The ends must be nodes, so only whole numbers of half-wavelengths fit — these are the harmonics. The nth harmonic has n antinodes and (n+1) nodes, wavelength 2L/n and frequency n times the fundamental. The whole pattern stays put and just breathes up and down; energy is stored, not carried along.

• Try this: Step through the harmonics — count the antinodes (n) and nodes (n+1).
• Try this: Turn on the component waves and watch the blue and green travelling waves add to the standing pattern.
• Try this: Raise the wave speed — for the same harmonic, frequency rises (v = fλ).
• Try this: Notice the fixed ends are always nodes — that is what quantises the harmonics.