Trane TRG-TRC007-EN manual Logarithmic Scale, Fundamentals of Sound, period one, ratio, 10 ´ log10

period one

Fundamentals of Sound

notes

Logarithmic Scale

ratio	log10	10 ´ log10
1	0	0
10	1	10
100	2	20
1,000	3	30
10,000	4	40
100,000	5	50
1,000,000	6	60
10,000,000	7	70
100,000,000	8	80
1,000,000,000	9	90
		Figure 14

A logarithm is the exponent power of the base. In this case, the base is ten. For example, the log10 of 10 (or 101) equals 1, the log10 of 100 (or 102) equals 2, and the log10 of 1,000,000,000 (or 109) 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 log10 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).

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