In Physical, a vector of wave (or “vector of phase”, in electronics in particular) is as its name indicates it a Vecteur representing a Onde. The standard of the vector corresponds to the Nombre of wave (dependant contrary to the Wavelength), and its direction indicates the direction of propagation of the Onde.

The vector of wave is very useful to generalize the equation of a Onde with the description of a family of waves. If all the waves of a family are propagated in the same direction and have same the Wavelength, they all can be described by the same vector of wave. The case more the current of a family of wave observing these conditions is that of a plane Onde, for which the family of waves is also coherent (all the waves have same the phase).

For example, a current representation of a wave in a point of space is:

$\backslash \; psi\; \backslash \; left\; (T\; \backslash \; right)\; =\; has\; \backslash \; cos\; \backslash \; left\; (\backslash \; phi\; +\; \backslash \; Omega\; T\; \backslash \; right)\; \backslash ,$

• has is the amplitude of the wave.
• ω is the angular Fréquence or pulsation.
• φ is the Déphasage of the wave.
• T is the variable time.

To generalize this equation at all the points of a unidimensional space in the direction of propagation, it is necessary to add a second term of Déphasage:

$\backslash \; psi\; \backslash \; left\; (T,\; Z\; \backslash \; right)\; =\; has\; \backslash \; cos\; \backslash \; left\; (\backslash \; phi\; -\; K\; Z\; +\; \backslash \; Omega\; T\; \backslash \; right)\; \backslash ,$

• K is the Nombre of wave.
• Z is the variable of space in the direction of propagation.

In the case of a space with three dimensions and in the case of Onde planes S, it is easy to generalize the preceding formula by replacing the Nombre of wave K by the vector of wave: $\backslash \; vec\; k$, and the variable of space Z by the vector position: $\backslash vec\; r$:

$\backslash \; psi\; \backslash \; left\; (T,\; \{\backslash \; mathbf\; R\}\; \backslash \; right)\; =\; has\; \backslash \; cos\; \backslash \; left\; (\backslash \; phi\; -\; \{\backslash \; mathbf\; K\}\; \backslash \; cdot\; \{\backslash \; mathbf\; R\}\; +\; \backslash \; Omega\; T\; \backslash \; right)\; \backslash ,$

The reasoning is similar for waves " not planes" , but with an amplitude has depend on the position.

See too

• Wave

• Number of reciprocal wave
• Space