It is not unusual for the phase speed of a wave to depend on the frequency or wavelength of the wave, in certain media. In these media, the function ω(k) is called a “dispersion relation,” and the medium is called dispersive. In such a material, information and energy are usually transported at the group velocity, whose magnitude is given by

It is also not unusual for the group velocity to be in the opposite direction to the phase velocity of the individual waves: