Displacement in standing wave
=============================

A *standing*, or *stationary*, *wave* is the result of the interference of two identical waves
moving in opposite directions.

**Notes:**

#. In this law we assume the standing wave to be composed of two identical traveling sinusoidal
   waves of the form :math:`u_\text{max} \sin(k x \pm \omega t)`
#. A standing wave is no longer a traveling one because it doesn't move in a single direction.

**Links:**

#. `Physics LibreTexts, similar to formula 14.7.3 <https://phys.libretexts.org/Bookshelves/University_Physics/Book%3A_Introductory_Physics_-_Building_Models_to_Describe_Our_World_(Martin_Neary_Rinaldo_and_Woodman)/14%3A_Waves/14.07%3A_Standing_waves>`__.

.. py:currentmodule:: symplyphysics.laws.waves.displacement_in_standing_wave

.. py:data:: total_displacement

    Displacement of the resulting wave.

    Symbol:
        :code:`u`

    Latex:
        :math:`u`


.. py:data:: amplitude

    Amplitude of the interfering waves.

    Symbol:
        :code:`u_max`

    Latex:
        :math:`u_\text{max}`


.. py:data:: angular_wavenumber

    :attr:`~symplyphysics.symbols.classical_mechanics.angular_wavenumber` of the interfering waves.

Symbol:
    :code:`k`

Latex:
    :math:`k`

Dimension:
    :code:`angle/length`


.. py:data:: position

    :attr:`~symplyphysics.symbols.classical_mechanics.position`, or spatial coordinate.

Symbol:
    :code:`x`

Latex:
    :math:`x`

Dimension:
    :code:`length`


.. py:data:: angular_frequency

    :attr:`~symplyphysics.symbols.classical_mechanics.angular_frequency` of the interfering waves.

Symbol:
    :code:`w`

Latex:
    :math:`\omega`

Dimension:
    :code:`angle/time`


.. py:data:: time

    :attr:`~symplyphysics.symbols.basic.time`.

Symbol:
    :code:`t`

Latex:
    :math:`t`

Dimension:
    :code:`time`


.. py:data:: law

    :code:`u = 2 * u_max * sin(k * x) * cos(w * t)`

    Latex:
        .. math::
            u = 2 u_\text{max} \sin(k x) \cos(\omega t)