Acoustical Porous Material Recipes

A few comments

When impacting the interface between 2 different media (or a change in the propagation medium), a wave (or a part of this wave) undergoes reflection and/or refraction.
The graphic used here shows the specular reflection of a ray (in opposition to a diffuse reflection occurring when the wavelength is not much larger compared to the interface heterogeneities).
A larger discussion about specular reflection and refraction (with interactive graphics) can be found in the APMR page about variational principles.

The refraction obeys a simple rule : the incident & reflected rays lie in the same plane and the incident & the reflected angles, with respect to the normal of the interface, verifies the equation :
\[ n_1 \sin \theta_1 = n_2 \sin \theta_2 \] where $n_1$ is the refraction index in one medium, $n_2$ is the refraction index in the other medium. $\theta_1$ and $\theta_2$ are the angles, with respect to the normal of the interface.
This equation is known as the Snell, Snell-Descartes or Ibn Sahl equation.

Materials with negative refraction indices (theorized in the mid-20th century and physically developed since the very end of the 20th century) is currently an active research field, sometimes referred to as meta-materials. These materials allow to hide "usual" materials (with positive refraction indices, usually higher than 1) from the waves propagating through them. In such an application, the difficult part is also to introduce as less dissipation as possible in the materials with negative refraction indices to perform an effective cloaking.

Refraction should not be confused with Diffraction for which the wave propagates in a medium but can be perturbed due to the presence of another medium (depending on the wavelength of the wave).

Transmission is the term to use when a wave pass through a medium $\textcolor{#69cad3}{\blacksquare}$ (or a group of media). Here the animation shows the common case of a medium $\textcolor{#69cad3}{\blacksquare}$ with a refraction index larger than the one of the original medium $\square$.

2 refractions take place in the graphic : one at each interfaces (between medium $\square$ & $\textcolor{#69cad3}{\blacksquare}$ and between media $\textcolor{#69cad3}{\blacksquare}$ & $\square$). As a result, the path followed by the wave is not a straight line.

The term transmission is used when the wave passes through a medium. Note that doing so, the wave encounters two interfaces (one when entering the medium, the other one when leaving the medium) and thus can be subjected twice to reflection and refraction.
In addition, when propagating through the medium, other phenomena can occur (like absorption, dispersion, scattering...).

Absorption, or dissipation, denotes the fact that a wave can loose a part of its energy in a medium. This energy is eventually converted into heat from different phenomena (in vibro-acoustics : viscous and thermal effects when propagating in a fluid phase and structural damping when propagating in a solid phase).
Absorption is a frequency depend phenomenon : the amount of energy dissipated depends on the frequency of the wave. Absorption is thus linked to dispersion following Kramers-Kronig relations (i.e. Hilbert's transform).

Note that the word "absorption" is also used in chemistry and everyday life when molecules of a medium in one state are incorporated into another medium in a different state (e.g. a liquid is absorbed by a solid). This absorption phenomenon is not considered as a wave phenomenon and should not be confused with the "absorption" described above for waves.

Scattering occurs when the wavelength of a wave propagating through a medium is not much larger compared to heterogeneities in that medium (i.e. the medium is not seen by the wave as an homogeneous one). Different theories have been developed to account for the scattering of waves.

Sorption is a broad term used to describe the physical and chemical processes involved when molecules of a medium are becoming attached to, detached from or incorporated in another medium.
The animation of this page shows the particular case of molecules ($\textcolor{#c74863}{\bullet}$) being attached to : adsorption, and detached from : desorption, another medium ($\textcolor{#69cad3}{\blacksquare}$).

The content of this page is copyleft under :
the creative commons license Attribution 3.0 Unported (CC BY 3.0).
Luc Jaouen (@ljaouen), ISSN 2606-4138.
Site hosted by Matelys.