Wavelength in rectangular waveguide
===================================

Wavelength in a rectangular waveguide is a function of operating wavelength (or
wavelength in free space) and the critical (or lower cutoff) wavelength, and is
always longer than that in free space.

**Links:**

#. `Microwaves101, section "Guide Wavelength" <https://www.microwaves101.com/encyclopedias/waveguide-mathematics>`__.

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

.. py:data:: waveguide_wavelength

    Guide :attr:`~symplyphysics.symbols.classical_mechanics.wavelength` is defined as the distance between the two equal phase planes along the
    waveguide.

Symbol:
    :code:`lambda_g`

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

Dimension:
    :code:`length`


.. py:data:: vacuum_wavelength

    :attr:`~symplyphysics.symbols.classical_mechanics.wavelength` of the signal wave in vacuum.

Symbol:
    :code:`lambda`

Latex:
    :math:`\lambda`

Dimension:
    :code:`length`


.. py:data:: critical_wavelength

    Critical :attr:`~symplyphysics.symbols.classical_mechanics.wavelength` of 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:: law

    :code:`lambda_g = lambda / sqrt(1 - (lambda / lambda_c)^2)`


    Latex:
        .. math::
            \lambda_\text{g} = \frac{\lambda}{\sqrt{1 - \left(\frac{\lambda}{\lambda_\text{c}}\right)^{2}}}