Wave equation in one dimension
==============================

The *wave equation* is a second-order linear partial differential equation used to
describe the propagation of waves, including standing wave fields such as mechanical
or electromagnetic waves.

**Notes:**

#. This equation is called one-dimensional because the displacement function depends
   only on one spatial dimension.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Wave_equation#Wave_equation_in_one_space_dimension>`__.

.. py:currentmodule:: symplyphysics.definitions.wave_equation_in_one_dimension

.. py:data:: position

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

Symbol:
    :code:`x`

Latex:
    :math:`x`

Dimension:
    :code:`length`


.. py:data:: time

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

Symbol:
    :code:`t`

Latex:
    :math:`t`

Dimension:
    :code:`time`


.. py:data:: displacement

    Factor representing a displacement from rest position, which could be
    pressure, position, electric field, etc., as a function of position
    and time.

Symbol:
    :code:`u(x, t)`

Latex:
    :math:`u{\left(x,t \right)}`

Dimension:
    :code:`any_dimension`


.. py:data:: phase_speed

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

Symbol:
    :code:`v`

Latex:
    :math:`v`

Dimension:
    :code:`velocity`


.. py:data:: definition

    :code:`Derivative(u(x, t), (x, 2)) = Derivative(u(x, t), (t, 2)) / v^2`


    Latex:
        .. math::
            \frac{\partial^{2}}{\partial x^{2}} u{\left(x,t \right)} = \frac{\frac{\partial^{2}}{\partial t^{2}} u{\left(x,t \right)}}{v^{2}}