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12 TRG-TRC007-EN
notes
period one
Fundamentals of Sound
A logarithm is the exponent power of the base. In this case, the base is ten. For
example, the log
10
of 10 (or 10
1
) equals 1, the log
10
of 100 (or 10
2
) equals 2, and
the log
10
of 1,000,000,000 (or 10
9
) equals 9.
As mentioned earlier, the loudest sound the human ear can hear without
damage due to prolonged exposure is about 1,000,000,000 times greater than
the quietest perceptible sound. If we use the quietest perceptible sound as the
reference value, this ratio would range from 1 to 1,000,000,000. Converting this
arithmetic range to a log
10
scale yields a range of 0 to 9. This unitless result is
described in terms of bels. Multiplying by ten results in the more-commonly
used broader range of 0 to 90 decibels (dB
).
Logarithmic Scale
ratio
1
10
100
1,000
10,000
100,000
1,000,000
10,000,000
100,000,000
1,000,000,000
ratio
1
10
100
1,000
10,000
100,000
1,000,000
10,000,000
100,000,000
1,000,000,000
log
10
0
1
2
3
4
5
6
7
8
9
log
10
0
1
2
3
4
5
6
7
8
9
10 ´
´´
´ log
10
0
10
20
30
40
50
60
70
80
90
10 ´
´´
´ log
10
0
10
20
30
40
50
60
70
80
90
Figure 14