Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
this type of decibel so commonly that the SPL is often dropped off and simply dB is used where
the context is clear. You learn that human speech is about 60 dB, rock music is about 110 dB,
and the loudest thing you can listen to without hearing damage is about 120 dB – all of these
measurements implicitly being dBSPL.
The definition of intensity decibels, dBSIL, is mostly of interest to help us understand
how the definition of dBSPL can be derived from dBPWL. We’ll also use the definition of
intensity decibels in an explanation of the inverse square law, a rule of thumb that helps us
predict how sound loudness decreases as sound travels through space in a free field (Section
There’s another commonly-used type of decibel that you’ll encounter in digital audio
software environments – the decibel-full-scale (dBFS). You may not understand this type of
decibel completely until you’ve read Chapter 5 because it’s based on how audio signals are
digitized at a certain bit depth (the number of bits used for each audio sample). We’ll give the
definition here for completeness and revisit it in Chapter 5. The definition of dBFS uses the
largest-magnitude sample size for a given bit depth as its reference point. For a bit depth of n,
this largest magnitude would be .
where n is a given bit depth and is an integer sample value between and
Equation 4.8 Decibels-full-scale, abbreviated dBFS
Figure 4.2 shows an audio processing environment where a sound wave is measured in
dBFS. Notice that since | | is never more than , (
) is never a positive number.
When you first use dBFS it may seem strange because all sound levels are at most 0. With
dBFS, 0 represents maximum amplitude for the system, and values move toward as you
move toward the horizontal axis, i.e., toward quieter sounds.
Figure 4.2 Sound amplitude measured in dBFS