Plane Wave Reflection at an Infinitely Thick Porous Layer

“Porous layer” here stands for any homogeneous, isotropic material with characteristic propagation constant $\Gamma _{a}$ and wave impedance $Z_{a}$. If the material is air, then $\Gamma _{a}\to jk_{0}$; $Z_{a}\to Z_{0}$.

Sound incidence is as in → Sect.  D.1 .

Sound field above absorber: p${}_{{1}}$=p${}_{{i}}$+p${}_{{r}}$ (as in → Sect.  D.1 )?,

sound field in absorber: $p_{2}(x,y)=p_{t}(x,y)=B\cdot e^{{\scriptsize-\Gamma _{a}\left({x\cos\Theta _{a}+y\sin\Theta _{a}}\right)}}$?. (1)

The boundary conditions are:

•?Equal propagation constant in y direction on both sides;

•?Equal normal admittance component on both sides (is equivalent to matching sound pressure and normal particle velocity).

Refracted angle $\Theta$ ${}_{{a}}$ (complex!): $\displaystyle\frac{\sin\Theta _{a}}{\sin\Theta}=\displaystyle\frac{j\, k_{0}}{\Gamma _{a}}$?. (2)

Reflection factor r: \(\displaystyle r=\frac{Z_{a}/\cos\Theta _{a}-Z_{0}/\cos\Theta}{Z_{a}/\cos\Theta...