7.1.2. Sound Power, Sound Pressure and Sound Level

A sound source can be assigned a sound power, which is a fixed value that is independent of the position and distance of the receiver. The sound pressure, on the other hand, changes due to obstacles in the room and the distance of the receiver from the source, and is therefore a location-dependent value.

Since very large numerical ranges are relevant for sound pressure and sound power, the decibel, a logarithmic ratio, was introduced. The following applies to the sound pressure level:

 L_p=10\cdot\log\frac{p^2}{p_0^2}=20\cdot\log\frac{p}{p_0}

For the sound power level applies:

L_W=10\cdot\log{\frac{P}{P_0}}

Thereby sound pressure p_ , reference sound pressure  p_{_0}=2\cdot10^{-5}  Pa and the sound power P, reference sound power P_0=10^{-12} W.

The reference values represent the hearing threshold of the human ear at frequency 1 kHz.

If several sound sources of the number  z of the same level are considered, the level change is calculated with (see Figure 7.1.2.a):

\Delta L=10\cdot\log{z}

Figure 7.1.2.a Level increase for identical sound sources

For two sound sources of different levels with L_1>L_2 the level change is calculated with (see Figure 7.1.2b):

\Delta L=10\cdot\log{\left(1+10^{0,1\cdot\left(L_2-L_1\right)\right)})}

Figure 7.1.2.b: Level increase for different sound sources

If several sound sources of different levels are present, the sum level is calculated as well: 

L_{ges}=10\cdot\log{\sum_{i=1}^{i=z}10^{0,1\cdot L_i}}

For a level averaging applies:
L_m=10\cdot\log{\left(\frac{1}{z}\cdot\sum_{i=1}^{i=z}10^{0,1\cdot L_i}\right)}

f(x) = \sin x