Wavelength of standing wave in string with fixed ends
=====================================================

If a standing wave occurs in a string with fixed ends, the value of the displacement
function :math:`q(x)` must be zero on both ends of the string. To satisfy this boundary
condition, only an integer number of half-waves can fit into the total length of the
string.

**Conditions:**

#. Boundary condition: :math:`q(0) = q(L) = 0`.

**Links:**

#. `Wikipedia <https://en.wikipedia.org/wiki/Standing_wave#Standing_wave_on_a_string_with_two_fixed_ends>`__.

.. py:currentmodule:: symplyphysics.laws.waves.wavelength_of_standing_wave_in_string_with_fixed_ends

.. py:data:: integer_factor

    Positive integer, also called *harmonic number* of the :math:`n`-th harmonic.
    See :attr:`~symplyphysics.symbols.basic.positive_number`.

Symbol:
    :code:`N`

Latex:
    :math:`N`

Dimension:
    :code:`dimensionless`


.. py:data:: wavelength

    :attr:`~symplyphysics.symbols.classical_mechanics.wavelength` of standing wave.

Symbol:
    :code:`lambda`

Latex:
    :math:`\lambda`

Dimension:
    :code:`length`


.. py:data:: string_length

    :attr:`~symplyphysics.symbols.classical_mechanics.length` of the string.

Symbol:
    :code:`l`

Latex:
    :math:`l`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`N * lambda / 2 = l`


    Latex:
        .. math::
            \frac{N \lambda}{2} = l