Resonant frequency of rectangular resonator
===========================================

A rectangular resonator consists of metal walls and a material filling it.

**Notation:**

#. :math:`c` (:code:`c`) is :attr:`~symplyphysics.quantities.speed_of_light`.

**Links:**

#. `Mahatma Gandhi Central University, formula 17 on page 12 (PDF file) <https://mgcub.ac.in/pdf/material/20200427120209be39415ad1.pdf>`__.

.. py:currentmodule:: symplyphysics.laws.electricity.circuits.resonators.resonant_frequency_of_rectangular_resonator

.. py:data:: resonant_frequency

    Resonant :attr:`~symplyphysics.symbols.classical_mechanics.temporal_frequency` of the resonator.

Symbol:
    :code:`f_r`

Latex:
    :math:`f_\text{r}`

Dimension:
    :code:`frequency`


.. py:data:: first_index

    Index that changes along the :attr:`~width` of the resonator, see
    :attr:`~symplyphysics.symbols.basic.positive_number`.

Symbol:
    :code:`m`

Latex:
    :math:`m`

Dimension:
    :code:`dimensionless`


.. py:data:: second_index

    Index that changes along the :attr:`~height` of the resonator, see
    :attr:`~symplyphysics.symbols.basic.positive_number`.

Symbol:
    :code:`n`

Latex:
    :math:`n`

Dimension:
    :code:`dimensionless`


.. py:data:: third_index

    Index that changes along the :attr:`~length` of the resonator, see
    :attr:`~symplyphysics.symbols.basic.positive_number`.

Symbol:
    :code:`p`

Latex:
    :math:`p`

Dimension:
    :code:`dimensionless`


.. py:data:: width

    :attr:`~symplyphysics.symbols.classical_mechanics.length` of the resonator along the axis perpendicular to the axis of wave
    propagation and to :attr:`~height`.

Symbol:
    :code:`l_1`

Latex:
    :math:`l_{1}`

Dimension:
    :code:`length`


.. py:data:: height

    :attr:`~symplyphysics.symbols.classical_mechanics.length` of the resonator along the axis perpendicular to the axis of wave
    propagation and to :attr:`~width`.

Symbol:
    :code:`l_2`

Latex:
    :math:`l_{2}`

Dimension:
    :code:`length`


.. py:data:: length

    :attr:`~symplyphysics.symbols.classical_mechanics.length` of the resonator along the axis of wave propagation.

Symbol:
    :code:`l_3`

Latex:
    :math:`l_{3}`

Dimension:
    :code:`length`


.. py:data:: relative_permittivity

    :attr:`~symplyphysics.symbols.electrodynamics.relative_permittivity` of the medium filling the resonator.

Symbol:
    :code:`epsilon_r`

Latex:
    :math:`\varepsilon_\text{r}`

Dimension:
    :code:`dimensionless`


.. py:data:: relative_permeability

    :attr:`~symplyphysics.symbols.electrodynamics.relative_permeability` of the medium filling the resonator.

Symbol:
    :code:`mu_r`

Latex:
    :math:`\mu_\text{r}`

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`f_r = c / (2 * sqrt(epsilon_r * mu_r)) * sqrt((m / l_1)^2 + (n / l_2)^2 + (p / l_3)^2)`


    Latex:
        .. math::
            f_\text{r} = \frac{c}{2 \sqrt{\varepsilon_\text{r} \mu_\text{r}}} \sqrt{\left(\frac{m}{l_{1}}\right)^{2} + \left(\frac{n}{l_{2}}\right)^{2} + \left(\frac{p}{l_{3}}\right)^{2}}