Dispersion relation

When dealing with several coupled oscillators, the system exhibits normal modes (decoupled oscillators), each with a distinct spatial frequency, which describes the wavelength of the oscillation across the system, i.e., the shape of the normal mode when seen from the point of view of positions.
If we interpret the system as decoupled oscillators, the temporal frequency of each oscillator/normal mode is related to its spatial frequency.
The relationship between spatial frequency $k$ (wave number) and temporal frequency $\omega$ is given by a dispersion relation, which depends on the system's physical properties.