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Definition of the most important sound
levels
Sound pressure level L p
The sound pressure level is defined as the twentyfold
decade logarithm of the ratio that results from the effective
value of the sound pressure and the reference sound
pressure. The reference sound pressure is, as already
mentioned, defined as p0 = 0,00002 Pa = 20 μPa.
Lp = 20×
lg(
p = 0,
00002Pa
0
Issue 04 | 2010
p
p
0
)
Lp[
dB]
p[
Pa]
p = 0,
00002 × 10
The sound pressure level is a measurand, always to be
indicated with the distance from the source of sound.
Sound power level L W
The sound power level is defined as the tenfold decade
logarithm of the ratio that results from the sound power
and the reference sound power. As reference sound power
is fixed P0 = 10-12 W = 1pW. The reference value of the
sound power results from the reference sound pressure
according to
2
p0
P0
= × S0
=
ρ × c
L W
P
0
⎛
= 10×
lg
⎜
⎝
= 10
−12
W
P
P
0
⎞
⎟
⎠
−5
2
( 2× 10 ) −12
× 1m²
= 10 W
4×
10
2
L W
[ dB]
P[
W ]
The sound power level is often used to describe by
means of only one numerical value the sound produced
by a machine or a plant. At this point, it has to be pointed
out that the difference between sound pressure level and
sound power level must be absolutely clear. The indication
of the sound pressure level requires the indication of the
distance from the test object too.
Calculation by using levels
Having to do with levels and comparative values in dB
is not easy at first. But after some time it will become a
habit with them, because dealing with levels is very simple
and has certain advantages, provided that the range of
levels is not exceeded. It is only the conversion in absolute
pressures and powers that requires the knowledge of
logarithmic laws. Equal, relative changes in dB get always
expressed by equal dB-differences
Lp
20
TRANSFER OF TECHNOLOGY
Energetic linkage of levels with equal
reference value
The addition or the separation of different sound portions
from each other must on principle take place by intensities,
powers or energies that belong to them. For it we make a
distinction between the following operations:
• Energetic addition of levels
• Energetic averaging of levels
• Energetic subtraction of levels
The applications in which we are interested are:
• the addition of several sources of sound to which a
measuring point is exposed simultaneously,
• the addition of several measuring points on an enveloping
surface to determine the sound power of a source of
sound, and
• the addition via the frequency to enable the third-octave
spectrum to be converted into the octave spectrum,
or to calculate the total sound level resulting from the
frequency spectrum.
The addition via time to form the averaging- or rating
sound level and the sound exposition level are not of
interest here. The sound level meters common today
automatically form the average value of time and register
the bar maximum value within the averaging period of
time.
n
∑
i=
1
10
Summenpegel L = 10×
lg( 10 )
Mittelungspegel
Σ
n Li
1
Lm = 10×
lg( ∑
m Σ
n i=
1
L i
10 10 ) ⇒ L = L −10×
lg n
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