Critical wavelength in rectangular waveguide
============================================

A rectangular waveguide is a rectangular metal waveguide capable of supporting waves
propagating along it. The critical frequency depends on the indices of the specific
propagation mode and the dimensions of the waveguide cross-section.

..
    TODO: find link

.. py:currentmodule:: symplyphysics.laws.electricity.circuits.waveguides.critical_wavelength_in_rectangular_waveguide

.. py:data:: critical_wavelength

    Critical :attr:`~symplyphysics.symbols.classical_mechanics.wavelength` in the waveguide. See :ref:`Critical wavelength of waveguide <critical_wavelength_waveguide_def>`.

Symbol:
    :code:`lambda_c`

Latex:
    :math:`\lambda_\text{c}`

Dimension:
    :code:`length`


.. py:data:: first_index

    The first index shows how many half-wavelengths fit across the width of the cross
    section.

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`dimensionless`


.. py:data:: second_index

    The second index shows how many half-wavelengths fit across the height of the cross
    section.

Symbol:
    :code:`n`

Latex:
    :math:`n`

Dimension:
    :code:`dimensionless`


.. py:data:: width

    Width, or first dimension of the cross section. See :attr:`~symplyphysics.symbols.classical_mechanics.length`.

Symbol:
    :code:`a`

Latex:
    :math:`a`

Dimension:
    :code:`length`


.. py:data:: height

    Height, or second dimension of the cross section. See :attr:`~symplyphysics.symbols.classical_mechanics.length`.

Symbol:
    :code:`b`

Latex:
    :math:`b`

Dimension:
    :code:`length`


.. py:data:: law

    :code:`lambda_c = 2 / sqrt((m / a)^2 + (n / b)^2)`


    Latex:
        .. math::
            \lambda_\text{c} = \frac{2}{\sqrt{\left(\frac{m}{a}\right)^{2} + \left(\frac{n}{b}\right)^{2}}}