# Group Velocity

The group velocity of a wave is the velocity with which the overall shape of the waves' amplitudes — known as the modulation or envelope of the wave — propagates through space.

For example, imagine what happens if a stone is thrown into the middle of a very still pond. When the stone hits the surface of the water, a circular pattern of waves appears. It soon turns into a circular ring of waves with a quiescent center. The ever expanding ring of waves is the wave group, within which one can discern individual wavelets of differing wavelengths traveling at different speeds. The longer waves travel faster than the group as a whole, but they die out as they approach the leading edge. The shorter waves travel more slowly and they die out as they emerge from the trailing boundary of the group.

### Other articles related to "group velocity, group, velocity":

Billow - Mathematical Description of One-dimensional Waves - Amplitude and Modulation
... If the group velocity (see below) is wavelength-independent, this equation can be simplified as showing that the envelope moves with the group velocity and ... Otherwise, in cases where the group velocity varies with wavelength, the pulse shape changes in a manner often described using an envelope equation ...
Vertically Propagating Rossby-gravity Waves
... On a typical "m,k" dispersion diagram, the group velocity (energy) would be directed at right angles to the n = 0 (mixed Rossby-gravity waves) and n = 1 (gravity or Rossby waves) curves and ... Typical group velocities for each component are the following 1 cm/s for gravity waves and 2 mm/s for planetary (Rossby) waves. 10,000 km), vertical wavelengths of 4–8 km, and upward group velocity ...
Dispersion (optics)
... In optics, dispersion is the phenomenon in which the phase velocity of a wave depends on its frequency, or alternatively when the group velocity depends on the frequency ... chromatic dispersion to emphasize its wavelength-dependent nature, or group-velocity dispersion (GVD) to emphasize the role of the group velocity ...
Wave Propagation - Wave Velocity
... Further information phase velocity, group velocity, and signal velocity Wave velocity is a general concept, of various kinds of wave velocities, for a wave's phase and speed concerning ... The phase velocity is given as where vp is the phase velocity (in meters per second, m/s), ω is the angular frequency (in radians per second, rad/s), k is the wavenumber (in radians per meter, rad/m) ... at which a resultant wave packet from a narrow range of frequencies will travel is called the group velocity and is determined from the gradient of the dispersion relation In almost all cases, a ...
Matter-wave Group Velocity
... The velocity of a particle, he concluded then (but may be questioned today, see above), should always equal the group velocity of the corresponding wave ... follows that where is the mass of the particle and v its velocity ... of light in a vacuum, is the Lorentz factor, and v is the velocity of the particle regardless of wave behavior ...

### Famous quotes containing the word group:

The government of the United States at present is a foster-child of the special interests. It is not allowed to have a voice of its own. It is told at every move, “Don’t do that, You will interfere with our prosperity.” And when we ask: “where is our prosperity lodged?” a certain group of gentlemen say, “With us.”
Woodrow Wilson (1856–1924)