Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
volume” by a certain air pressure amplitude wouldn't give much information about how much
louder it’s going to sound. Talking about loudness-changes in terms of decibels communicates
Change of sound amplitude How it is perceived in human hearing
1 dB smallest perceptible difference in loudness, only perceptible in acoustically-
insulated noiseless environments
3 dB smallest perceptible change in loudness for most people in real-world
+10 dB an approximate doubling of loudness
10 dB change
an approximate halving of loudness
Table 4.2 How sound level changes in dB are perceived
You may have noticed that when we talk about a “decibel change,” we refer to it as
simply decibels or dB, whereas if we are referring to a sound loudness level relative to the
threshold of hearing, we refer to it as dBSPL. This is correct usage. The difference between 90
and 80 dBSPL is 10 dB. The difference between any two decibels levels that have the same
reference point is always measured in dimensionless dB. We’ll return to this in a moment when
we try some practice problems in Section 2.
188.8.131.52 Various Usages of Decibels
Now let’s look at the origin of the definition of decibel and how the word can be used in a
variety of contexts.
The bel, named for Alexander Graham Bell, was originally defined as a unit for
measuring power. For clarity, we’ll call this the power difference bel, also denoted
Equation 4.5 , power difference bel,
The decibel is 1/10 of a bel. The decibel turns out to be a more useful unit than the bel
because it provides better resolution. A bel doesn’t break measurements into small enough units
for most purposes.
We can derive the power difference decibel ( ) from the power difference
bel simply by multiplying the log by 10. Another name for is dBPWL (decibels-
Equation 4.6 , abbreviated dBPWL
When this definition is applied to give a sense of the acoustic power of a sound, then
is the power of sound at the threshold of hearing, which is .
Sound can also be measured in terms of intensity. Since intensity is defined as power per
unit area, the units in the numerator and denominator of the decibel ratio are , and the
threshold of hearing intensity is . This gives us the following definition of
B, also commonly referred to as dBSIL (decibels-sound intensity level).