# Absorption Coefficient

As an incident wave hits a boundary, a part of it is reflected, as described by the reflection coefficient, and the rest of it is considered to be absorbed by the material at the boundary. Depending on the surface, a part of the energy might be transmitted through it and ideally this energy is accounted for in the absorption coefficients so that the relationship between absorption and reflection can be written as

We call $\alpha$ the (energy) absorption coefficient that describes how much of the power of the incident wave will be absorbed by boundary. The absorption coefficient thus has a direct relationship with the magnitude of the reflection coefficient but it does not include information regarding the phase shifts that occur at boundaries.

If $|R| = 1$, the material is fully reflecting but if $|R| = 0$, it is fully absorbing. The absorption coefficient is a very intuitive parameter and widely used in the acoustics community. Intuitively it ranges from 0 (no absorption) to 1 (or 100% or fully absorbed) and is always a real value. Good acoustic absorbers have high absorption coefficients.

Octave band absorption coefficients are the most frequently available data describing the acoustic properties of materials. It is thus unfortunate that they do not provide a rich enough description of how waves interact with them. We have, nonetheless, developed software to combat this and extract sensible phase information from a dataset of absorption coefficients (more here).

## Measurements

There can be plenty of reasons why absorption coefficients are the most commonly available acoustic data from material providers.

- They are very intuitive.
- It's the only input needed for geometrical acoustics solvers as they do not explicitly contain phase information.
- The measurement setup is quite standardized.

In the acoustics community, there are variants of the sound absorption coefficient, to name a few, Sabine absorption coefficients (outcome of ISO 354 [1] or ASTM C423 [2] measurements in reverberation chambers), practical absorption coefficients according to ISO 11654 [3] that are normally included in the manufacturer’s datasheet. Depending on the incidence direction of sound wave, normal incidence, oblique incidence, and random incidence absorption coefficients can be calculated.

These energy parameters are only suitable for GA simulation where the energy of sound is traced. Most measured absorption coefficients available for use in simulations are Sabine absorption coefficients, which is the absorption coefficient determined using two sets of reverberation time measurements according to ISO 354 in the one-third octave bands, or their simplified version called practical absorption coefficients in the octave bands. The reverberation chamber method is a convenient way to estimate the absorption characteristic of the specimen under test, but highly unreproducible and uncertain. The measured coefficients can have errors of about $\pm 0.2$ [4]. Note that Sabine absorption coefficients can be higher than 100 % (thus non-physical) and these absorption coefficients vary a lot depending on the reverberation chamber measured. Often it is still the most available data, so we have to make use of it. For real world applications, it is, however, important to keep in mind that the accuracy of those is limited and although simulations follow the input absorption perfectly, it may not match up with in-situ measurements.

A more informative quantity is the surface impedance. If those data are available, they should be used.

## References

[1] ISO 354:2003 Acoustics — Measurement of sound absorption in a reverberation room.

[2] ASTM C423-22 Standard Test Method for Sound Absorption and Sound Absorption Coefficients by the Reverberation Room Method.

[3] ISO 11654:1997 Acoustics — Sound absorbers for use in buildings — Rating of sound absorption.

[4] T. J. Cox, P. D'antonio. Acoustic absorbers and diffusers: theory, design and application. Crc Press, 2009.