Frequency shift from speed in arbitrary motion
==============================================

The *Doppler effect* or *Doppler shift* is the apparent change in frequency of a wave in
relation to an observer moving relative to the wave source.

Also see :doc:`laws.waves.frequency_shift_from_speed_in_collinear_motion`.

**Conditions:**

#. The source and observer speeds are less or equal to the wave speed. Otherwise emitted
   waves are left behind the source or never reach the observer.
#. The speeds are much less than the speed of light, i.e. this law is non-relativistic.

..
    TODO find link to law with both angles

.. py:currentmodule:: symplyphysics.laws.waves.frequency_shift_from_speed_in_arbitrary_motion

.. py:data:: observed_frequency

    Observed :attr:`~symplyphysics.symbols.classical_mechanics.temporal_frequency` of the wave.

Symbol:
    :code:`f_o`

Latex:
    :math:`f_\text{o}`

Dimension:
    :code:`frequency`


.. py:data:: source_frequency

    Wave :attr:`~symplyphysics.symbols.classical_mechanics.temporal_frequency` of the source.

Symbol:
    :code:`f_s`

Latex:
    :math:`f_\text{s}`

Dimension:
    :code:`frequency`


.. py:data:: wave_speed

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

Symbol:
    :code:`v`

Latex:
    :math:`v`

Dimension:
    :code:`velocity`


.. py:data:: source_speed

    Magnitude of the velocity vector of the source. See :attr:`~symplyphysics.symbols.classical_mechanics.speed`.

Symbol:
    :code:`v_s`

Latex:
    :math:`v_\text{s}`

Dimension:
    :code:`velocity`


.. py:data:: observer_speed

    Magnitude of the velocity vector of the observer. See :attr:`~symplyphysics.symbols.classical_mechanics.speed`.

Symbol:
    :code:`v_o`

Latex:
    :math:`v_\text{o}`

Dimension:
    :code:`velocity`


.. py:data:: source_angle

    :attr:`~symplyphysics.symbols.basic.angle` between the wave velocity and the source velocity.

Symbol:
    :code:`theta_s`

Latex:
    :math:`\theta_\text{s}`

Dimension:
    :code:`angle`


.. py:data:: observer_angle

    :attr:`~symplyphysics.symbols.basic.angle` between the wave velocity and the observer velocity.

Symbol:
    :code:`theta_o`

Latex:
    :math:`\theta_\text{o}`

Dimension:
    :code:`angle`


.. py:data:: law

    :code:`f_o = f_s * (v - v_o * cos(theta_o)) / (v - v_s * cos(theta_s))`


    Latex:
        .. math::
            f_\text{o} = \frac{f_\text{s} \left(v - v_\text{o} \cos{\left(\theta_\text{o} \right)}\right)}{v - v_\text{s} \cos{\left(\theta_\text{s} \right)}}