Reference problem
=====================


Geometry
---------


.. image:: images/1000000000000554000002E7A0F250415844FC36.png
    :width: 4.7563in
    :height: 2.5902in


.. _RefImage_1000000000000554000002E7A0F250415844FC36.png:

**Figure 1.1 Problem geometry and loading system**

Parallelipipedic cavity:


* length: :math:`L={l}_{x}=1.0m`


* height: :math:`h={l}_{y}=0.1m`


* width: :math:`l={l}_{z}=0.2m`

Coordinates of the points:


* :math:`A`: :math:`x=0.`, :math:`y=0.05`, :math:`z=0.1`


* :math:`B`: :math:`x=0.`, :math:`y=0.1`, :math:`z=0.2`


* :math:`C`: :math:`x=1.`, :math:`y=0.1`, :math:`z=0.0`


* :math:`D`: :math:`x=1.`, :math:`y=0.05`, :math:`z=0.1`


Material properties
----------------------

The material properties are those of air:


.. csv-table::

    ":math:`c=340{\text{m.s}}^{-1}` ", "Sound speed"
    ":math:`\rho =1.2{\text{kg.m}}^{-3}` ", "Density"



Boundary conditions and loads
-------------------------------------

Uniform unit speed and impedance:

.. csv-table::

    "Inlet section :math:`x=0` "," :math:`{V}_{n}=-1{\text{m.s}}^{-1}\text{à 500 Hz}`
    :math:`{Z}_{n}=-1000{\text{kg.m}}^{-2}\mathrm{.}\text{s}`"
    "Input section :math:`x=1` "," :math:`{Z}_{n}=-408{\text{kg.m}}^{-2}\mathrm{.}\text{s}`"