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 :ref:`scalar counterpart <Phase speed from angular frequency and wavenumber>` of
   this law.

**Links:**

#. `Wikipedia, derivable from here <https://en.wikipedia.org/wiki/Phase_velocity>`__.

.. py:currentmodule:: symplyphysics.laws.waves.vector.phase_velocity_from_angular_velocity_and_wavevector

.. py:data:: phase_velocity

    Vector of the phase velocity of the wave. See :attr:`~symplyphysics.symbols.classical_mechanics.phase_speed`.

Symbol:
    :code:`v`

Latex:
    :math:`{\vec v}`

Dimension:
    :code:`velocity`


.. py:data:: angular_frequency

    :attr:`~symplyphysics.symbols.classical_mechanics.angular_frequency` of the wave.

Symbol:
    :code:`w`

Latex:
    :math:`\omega`

Dimension:
    :code:`angle/time`


.. py:data:: angular_wavevector

    Angular wavevector of the wave. See :attr:`~symplyphysics.symbols.classical_mechanics.angular_wavenumber`.

Symbol:
    :code:`k`

Latex:
    :math:`{\vec k}`

Dimension:
    :code:`angle/length`


.. py:data:: phase_velocity_law_

    :code:`v = w / norm(k)^2 * k`


    Latex:
        .. math::
            {\vec v} = \frac{\omega}{\left \Vert {\vec k} \right \Vert^{2}} {\vec k}


.. py:data:: angular_wavevector_law

    :code:`k = w / norm(v)^2 * v`


    Latex:
        .. math::
            {\vec k} = \frac{\omega}{\left \Vert {\vec v} \right \Vert^{2}} {\vec v}