Mode

A mode is one of the discrete standing-wave patterns that a bounded system can support. For a string fixed at both ends, mode n has exactly n half-wavelengths between the ends, frequency n times the fundamental, and a specific spatial shape sin(n π x / L). The integer n is called the mode number.

Modes are the fundamental language of linear wave physics. Any motion of the system, no matter how complicated, is a superposition of modes — each oscillating independently at its own frequency. The modes form a basis for the space of all possible motions. This is true for strings, drums, organ pipes, crystals, and the electrons in atoms; the same integer labelling runs through the whole of modern physics.