Vectors - 3D Math Primer for Graphics and Game Development - page 42

the invention of the Kelvin scale by Lord Kelvin, that mankind finally had
an absolute temperature scale. 0 K is the coldest possible temperature,
corresponding to −273 o C.
Loudness. Loudness is usually measured in decibels (abbreviated dB). To
be more precise, decibels are used to measure the ratio of two power lev-
els. If we have two power levels P 1 and P 2 , then the difference in decibels
between the two power levels is
10 log 10 (P 2 /P 1 ) dB.
So, if P 2 is about twice the level of P 1 , then the difference is about 3 dB.
Notice that this is a relative system, providing a precise way to measure the
relative strength of two power levels, but not a way to assign a number to
one power level. In other words, we haven't established any sort of absolute
reference point. (It's also a logarithmic scale, but that isn't important here.)
You may have used a mixer board, volume control knob, or digital audio
program that measures volume in dB. Normally, there's an arbitrary point
marked 0 dB, and then most of the readings have negative values. In other
words, 0 dB is the loudest volume, and all other volume settings are softer.
None of these values are absolute—but how could they be? How could
your digital audio program know the absolute loudness you will experience,
which depends not only on the audio data, but also the volume setting on
your computer, the volume knob on your amplifier, the power supplied by
the amplifier to your speakers, the distance you are from the speakers, and
so on.
Sometimes people describe how loud something is in terms of an abso-
lute dB number. Following in the footsteps of Gabriel Fahrenheit, this scale
uses a reference point based on the human body. “Absolute” dB numbers
are actually relative to the threshold of hearing for a normal human. 6 Be-
cause of this, it's actually possible to have an “absolute” dB reading that
is negative. This simply means that the intensity is below the threshold
where most people are able to hear it.
At this point, we should probably mention that there is a way to devise
an absolute scale for loudness, by measuring a physical quantity such as
pressure, energy, or power, all of which have an absolute minimum value
6 About 20 micropascals. However, this number varies with frequency. It also increases
with age. One author remembers that when he was young, his father would never turn
the radio in the car completely off, but rather would turn the volume down below the
(father's) threshold of hearing. The son's threshold of hearing was just low enough for
this to be irritating. Today the son owns his own car and car radio, and has realized,
with some degree of embarrassment, that he also often turns the radio volume down
without turning it off. However, he offers in his defense that he turns it all the way
down, below everyone's threshold of hearing. (The other author wishes to suggest that
clearly even the term “normal human” is relative.)