1. Reference problem#

1.1. Geometry#

_images/10000F9000003417000010F37722B775931F4CD7.svg

Rectangular tube:

length:

\(L={l}_{x}=1.0m\)

height:

\(h={l}_{y}=0.1m\)

width:

\(l={l}_{z}=0.2m\)

Coordinates of the points (in \(m\)):

\(A\)

\(B\)

\(C\)

\(D\)

\(x\)

1.00

1.00

\(y\)

0.05

0.05

\(z\)

0.20

0.10

0.10

0.20

0.10

1.2. Material properties#

Air:

\(\rho =1.3\mathrm{kg.}{m}^{-3}\)

\(c=343.{\mathrm{m.s}}^{-1}\)

1.3. Boundary conditions and loading#

Normal incoming wave pressure

\({P}_{i}={P}_{0}\ast {e}^{i\omega t}\) With \({P}_{0}=1.0\mathrm{Pa}\)

Frequency

\(f=500\mathrm{Hz}\)

Impedance at the end \(\mathrm{CD}\)

\(Z=\rho c=445.9{\mathrm{kg.m}}^{-2}{s}^{-1}\)