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Decibel (dB)
dB is simply an abbreviation for the term decibel and one decibel is one tenth of
a Bel. The unit Bel is named after the scientist Alexander Graham Bell, but is
not widely used. A decibel value is dimensionless and is therefore not a value of
the measured quantity; it is a ratio of the measured quantity to a reference
quantity.
Choosing the reference quantity to be the quietest sound that can be detected
by a human ear (20µPa) we obtain a scale that expresses the measured sound
pressure level relative to the threshold of hearing.
It is a logarithmic form of a measurement that expresses the magnitude of a
physical quantity relative to a reference and is used commonly in electronics,
science and acoustics to measure the sound pressure level. The threshold of
hearing is therefore 0dB.
Lp
20 log
⋅
P
P
o
⋅
dB SPL
(
)
:=
The term dB(SPL) is generally abbreviated to just dB incorrectly giving the
impression that the dB is a unit in itself: -
Lp
20 log
⋅
P
P
o
⋅
dB
:=
Where Po is the reference sound pressure of 20µPa and P is the rms value of
the sound pressure measured.
One of the main benefits of using the decibel is its ability to represent very large
numbers with smaller more manageable ones.
The table below highlights this and shows the ratio of the measured quantity to a
reference, its scientific exponential form and its corresponding dB value using
the equation given above:-
Measured Ratio
Exponential Form
20 log
⋅
P
P
o
⋅
dB
1
10
0
0
10
10
1
20
100
10
2
40
1000
10
3
60
10000
10
4
80
100000
10
5
100
1000000
10
6
120
10000000
10
7
140
100000000
10
8
160
1000000000
10
9
180
10000000000
10
10
200
