Phase velocity from angular velocity and wavevector¶
The phase velocity of a wave is the rate at which the wave propagates in a medium. It is the velocity at which the phase of one frequency component of the wave travels. The phase velocity is collinear with the wavevector.
Notes:
Angular wavevector is a vector used in describing a wave. Its magnitude is the angular wavenumber of the wave. Its direction is perpendicular to the wavefront, and in isotropic media it is also the direction of wave propagation.
Also see the scalar counterpart of this law.
Links:
- phase_velocity¶
Vector of the phase velocity of the wave. See
phase_speed.
- Symbol:
v- Latex:
\({\vec v}\)
- Dimension:
velocity
- angular_frequency¶
angular_frequencyof the wave.
- Symbol:
w- Latex:
\(\omega\)
- Dimension:
angle/time
- angular_wavevector¶
Angular wavevector of the wave. See
angular_wavenumber.
- Symbol:
k- Latex:
\({\vec k}\)
- Dimension:
angle/length
- phase_velocity_law_¶
v = w / norm(k)^2 * k- Latex:
- \[{\vec v} = \frac{\omega}{\left \Vert {\vec k} \right \Vert^{2}} {\vec k}\]
- angular_wavevector_law¶
k = w / norm(v)^2 * v- Latex:
- \[{\vec k} = \frac{\omega}{\left \Vert {\vec v} \right \Vert^{2}} {\vec v}\]