Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013

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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

more.

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

environments

+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.

4.1.5.2 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-

power-level).

( )

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).