Groepsnelheid

In physics, particularly in the study of wave propagation, groepsnelheid (group velocity) is the speed at which the overall shape or envelope of a wave packet propagates through space. It represents the velocity at which the wave's energy or information is transmitted. This concept is distinct from the phase velocity, which is the speed at which any single frequency component of the wave travels.

The group velocity is crucially important in understanding how signals and wave pulses behave in dispersive media. A medium is dispersive when the phase velocity depends on the wave's frequency. In such media, individual frequency components of a wave packet travel at different speeds, causing the packet to spread out over time. The group velocity, mathematically defined as v_g = dω/dk, where ω is the angular frequency and k is the wave number, describes the motion of the pulse's peak.

In non-dispersive media, like a vacuum for light waves, the phase velocity and group velocity are identical. However, in many practical situations involving water waves, optical fibers, or sound waves in solids, dispersion occurs, making the group velocity the more relevant measure for signal speed.

A notable aspect is that in certain anomalous dispersion regions, the group velocity can exceed the speed of light in a vacuum or even become negative. It is essential to note that this does not violate causality, as the group velocity no longer corresponds to the signal velocity in such extreme conditions. The concept of group velocity is thus fundamental across various fields, including optics, acoustics, and quantum mechanics.