# Reflection Coefficient

The amplitude of a sound wave is reduced with a combination of geometrical spreading (sound intensity being proportional to the inverse of the square of the distance), attenuation (friction and relaxation processes in air), and boundary interactions. In this section we focus on the last point.

As waves hit boundaries they transmit through them, reflect off them, diffract around them and attenuate inside them. These various physical phenomena all influence the acoustics of rooms. We try to model these as accurately as possible, but to do so, it is important to think carefully about how we incorporate information related to boundary materials into our simulation engine. The pressure reflection coefficient describes how much of the wave energy reflects off the boundary as well as how it influences the phase of the reflected wave with respect to the incident wave. The pressure reflection coefficient gives the relative amplitude and phase of the reflected wave with respect to the incident pressure [1]

$R = \frac{p_{refl}}{p_{in}} =|R| exp(i\chi),$

where $\chi$ is the phase angle and $|R|$ is the relative magnitude of the reflected pressure, which can never take a value higher than one as that would mean that the surface of interest adds energy into the room, meaning the room is not a passive system any more.

## References​

[1] H. Kuttruff, Room acoustics. CRC Press, 2016.