Basic Documentation

Sound Measurement Parameters
We could improve the situation by using a direct comparison or ratio between the two
different sound power levels. For example, when comparing a normal voice to a whisper, we
could divide 10
-5
by 10
-9
that would yield 10,000. In other words, a normal voice has about
10,000 times more sound power than a whisper. This same approach would also tell us that
the sound power from a jetliner takeoff is 1,000,000,000 times more sound power than a
normal voice.
Unfortunately, these numbers are still awkward to work with because of the large number of
zeros. We can remove these zeros by using logarithms. Recall that a logarithm to the base
10 (or log for short), means that the power of 10 would be raised to become the number that
we’re concerned with. In other words, if we’re working with the number 10,000, the log is
simply 4, since 10
4
= 10,000. If we’re working with 1,000,000,000 the log would be 9 since
10
9
= 1,000,000,000.
Decibels
Using a comparison or ratio approach for large numbers tends to make it easier to relate to
the data. In addition, converting large numbers to logarithms further reduces the amount of
digits (and possible errors) when handling numbers comprised of many digits. This is where
the use of decibels offers a practical approach to quantifying sound parameters since a
decibel is based upon both a ratio and numbers converted into logarithms.
The first thing to note with regard to a decibel is that it expresses a ratio or makes a
comparison between two values; it is not a specific unit of measurement such as a watt,
pound, or even a foot of length. (Since decibels are based upon a ratio, they can be applied
to many other different scientific parameters besides sound.) Therefore, with regard to
applying decibels (dB), a reference point must be established as one component of the ratio.
With regard to sound power and sound pressure values, a bel is simply the logarithm of the
ratio of two different sound power or sound pressure levels. A decibel is 10 bels. (The reason
for using decibels instead of just staying with bels is that we do ourselves a favor by getting
rid of any decimals in the final values.) This may sound complicated and possibly somewhat
confusing, but you’ll understand it better after going through the process of establishing
decibels (dB) for the previous examples of a whisper, a normal voice, and the jetliner takeoff.
Then (hopefully) you’ll see the advantage of using dB instead of the large decimal numbers
that are required to express values in wattage.
Since we’re really only concerned with the sound that humans hear, we’ll use the threshold of
hearing as the common point of the comparison ratio. The sound power at the threshold of
hearing is generally accepted as 0.000000000001 watts (10
-12
watts), so this will always be
the reference point or one of the two parts to each sound power ratio.
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