Frequency shift from speed in collinear 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.

**Notes:**

#. When the source is moving with speed equal to wave speed, the observed frequency goes
   to infinity. This effect is known as the *sonic boom*.

**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 source and observer are moving directly towards or away from each other (collinear
   motion).

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Doppler_effect#General>`__.

.. py:currentmodule:: symplyphysics.laws.waves.frequency_shift_from_speed_in_collinear_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

    :attr:`~symplyphysics.symbols.classical_mechanics.speed` of the wave source, positive when moving away from the observer and negative otherwise.

Symbol:
    :code:`v_s`

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

Dimension:
    :code:`velocity`


.. py:data:: observer_speed

    :attr:`~symplyphysics.symbols.classical_mechanics.speed` of the observer, positive when moving away from the source and negative otherwise.

Symbol:
    :code:`v_o`

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

Dimension:
    :code:`velocity`


.. py:data:: law

    :code:`f_o = f_s * (v - v_o) / (v + v_s)`


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