Sound reflection factor

The sound reflection factor is a dimensionless quantity to describe the sound reflection at an interface , e.g. B. a wall or a transition to another medium . For a plane wave incident on the interface , it is defined as the ratio of the sound pressures p _{r of} the reflected wave and  p _{e of} the incident wave at the interface: ${\displaystyle r}$ 

${\displaystyle r=\left.{\frac {p_{\mathrm {r} }}{p_{\mathrm {e} }}}\right|_{\mathrm {Grenzfl{\ddot {a}}che} }}$

For the characteristic sound impedances  Z _{01 of} the transmission media in front of the interface and  Z ₀₂ behind the interface (in the case of a wall: wall impedance), there is the following relationship for perpendicular sound incidence:

${\displaystyle r={\frac {Z_{02}-Z_{01}}{Z_{02}+Z_{01}}}}$

Special cases:

• ${\displaystyle Z_{02}\rightarrow \infty }$: the sound reflection factor assumes its greatest possible value: r = 1 ( reverberant interface)
• ${\displaystyle Z_{02}=Z_{01}}$: the sound reflection factor becomes zero, i.e. i.e. there is no reflection; there is no interface.
• ${\displaystyle Z_{02}=0}$: r = −1 ( acoustically soft interface).

In the first and last case there is full reflection.

Sound reflection factor and sound insulation

The higher the sound reflection factor, degree or measure (see below), the better the sound insulation achieved , which, however, is also determined by other factors such as sound absorption . From the above In connection with this, it follows that for the most effective sound insulation possible (i.e. for the greatest possible reflection, which prevents sound transmission into the neighboring room), the values ​​of the characteristic sound impedances in front of and behind the interface should be as different as possible:

• For effective insulation of airborne sound (soft medium air in front of the interface), a material that is as hard and heavy as possible is recommended behind the interface
• on the other hand, when it comes to insulating structure-borne noise (hard medium in front of the interface), very soft insulation layers behind the interface often promise success.

Sound reflectance and sound reflection

The sound reflectance is a reflectance that is defined as the ratio of the sound intensities in the reflected sound wave and in the incident wave: ${\displaystyle \rho =r^{2}}$ ${\displaystyle I_{\mathrm {r} }}$ ${\displaystyle I_{0}}$

${\displaystyle \rho ={\frac {I_{\mathrm {r} }}{I_{0}}}}$

The corresponding measure is the sound reflection measure , given in decibels :

${\displaystyle r'=10\cdot \log \rho \;\,\mathrm {dB} }$