General solution to wave equation in one dimension
==================================================

Any function of a single variable can be a solution of the wave equation if it depends
on the phase of the wave, i.e. the position and time variables only appear in its
expression in the form of the :doc:`wave phase <laws.waves.phase_of_traveling_wave>`.

**Links:**

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

.. py:currentmodule:: symplyphysics.laws.waves.wave_equation_general_solution_in_one_dimension

.. py:data:: displacement

    Displacement from rest in the wave. Usually depends on position and time.

    Symbol:
        :code:`u`

    Latex:
        :math:`u`


.. py:data:: solution

    One-argument solution function of the wave equation.

    Symbol:
        :code:`f(phi)`

    Latex:
        :math:`f(\varphi)`


.. py:data:: wave_phase

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

Symbol:
    :code:`phi`

Latex:
    :math:`\varphi`

Dimension:
    :code:`angle`


.. py:data:: law

    :code:`u = f(phi)`

    Latex:
        .. math::
            u = f(\varphi)