Frequency shift from speed and angle
====================================

See :doc:`laws.waves.relativistic.longitudinal_frequency_shift_from_velocity`.

**Notes:**

#. It is not trivial to substitute moving source and idle observer with moving observer and idle source. Law
   depends on the current frame (observer or source are at rest at this frame), angle is detected at the point
   of emission or at the point of reception (see relativistic angle aberration).

**Conditions:**

#. Angle is measured at the moment of emission with respect to the observer frame.
#. Motion is in 2D space.

..
    TODO find link with angles

.. py:currentmodule:: symplyphysics.laws.waves.relativistic.frequency_shift_from_velocity_and_angle

.. py:data:: observer_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

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

Symbol:
    :code:`f_s`

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

Dimension:
    :code:`frequency`


.. py:data:: relative_speed

    Relative :attr:`~symplyphysics.symbols.classical_mechanics.speed` between the source and the observer.

Symbol:
    :code:`v`

Latex:
    :math:`v`

Dimension:
    :code:`velocity`


.. py:data:: source_angle

    :attr:`~symplyphysics.symbols.basic.angle` between the signal vector (directed from the source to the observer) and the source's velocity
    vector.

Symbol:
    :code:`phi`

Latex:
    :math:`\varphi`

Dimension:
    :code:`angle`


.. py:data:: law

    :code:`f_o = f_s * sqrt(c^2 - v^2) / (c - v * cos(phi))`


    Latex:
        .. math::
            f_\text{o} = \frac{f_\text{s} \sqrt{c^{2} - v^{2}}}{c - v \cos{\left(\varphi \right)}}