Sound Reflection and Scattering at Finite-Size Local Absorbers

The wording “local” in this heading (and at other places in this book) is a shorter form of “locally reacting”; the corresponding abbreviation for “bulk reacting” will be “lateral”.

If the side dimensions of the plane absorber are finite, scattering takes place at the borders between the absorber and the baffle wall. In fact, some theories determine the sound absorption of finite-size absorbers from the solution of the scattering problem.

Let the absorber with area A be in the plane ($x,y$); the z co-ordinate shows into the space above the absorber. The sketch shows co-ordinates and angles used, as well as the incident plane wave $p_{{i}}$ and the specularly reflected wave $p_{{r}}$. The field point is in P. Let s be a general co-ordinate.

Field composition: $p(s)=p_{i}(s)+p_{r}(s)+p_{s}(s)$

$$\begin{array}[]{@{}l@{\,}c@{\,}l}\displaystyle p_{i}(s)&=&P_{i}\cdot e^{{-j\,\left({k_{x}x+k_{y}y-k_{z}z}\right)}}\;,\\ \displaystyle...