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Wave speed is a wave property, which may refer to absolute value of: . phase velocity, the velocity at which a wave phase propagates at a certain frequency; group velocity, the propagation velocity for the envelope of wave groups and often of wave energy, different from the phase velocity for dispersive waves
For example, in the Cartesian ... For an incident wave traveling from one medium (where the wave speed is c 1) to another medium (where the wave speed is c 2), one ...
A soliton or solitary wave is a self-reinforcing wave packet that maintains its shape while it propagates at a constant velocity. Solitons are caused by a cancellation of nonlinear and dispersive effects in the medium. (Dispersive effects are a property of certain systems where the speed of a wave depends on its frequency.)
The phase velocity of a wave is the rate at which the wave propagates in any medium. This is the velocity at which the phase of any one frequency component of the wave travels. For such a component, any given phase of the wave (for example, the crest) will appear to travel at the phase velocity.
An example concerning the transmission of electromagnetic waves through an atomic gas is given by Loudon. [12] Another example is mechanical waves in the solar photosphere: The waves are damped (by radiative heat flow from the peaks to the troughs), and related to that, the energy velocity is often substantially lower than the waves' group ...
For example, if an electron wave packet is initially localized in a region of atomic dimensions (i.e., 10 −10 m) then the width of the packet doubles in about 10 −16 s. Clearly, particle wave packets spread out very rapidly indeed (in free space): [17] For instance, after 1 ms, the width will have grown to about a kilometer.
In this example, there are 5 + 3 / 4 waves between two wave group nodes in space, while there are 11 + 1 / 2 waves between two wave group nodes in time. North Pacific storm waves as seen from the NOAA M/V Noble Star, Winter 1989.
A wave along the length of a stretched Slinky toy, where the distance between coils increases and decreases, is a good visualization. Real-world examples include sound waves (vibrations in pressure, a particle of displacement, and particle velocity propagated in an elastic medium) and seismic P waves (created by earthquakes and explosions).