| I |
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| Io |
The human ear is actually an amazing instrument. It can handle sound with frequencies covering three orders of magnitude, and intensities covering 12 orders of magnitude!
The ear can do this because it responds to sound intensity logarithmically. This is why we use the decibel scale - much like the Richter scale for measuring earthquakes, the decibel scale is logarithmic.
| Sounds in decibels are given by: β | = (10 dB) * log | ( |
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where I is the intensity in W/m2 and Io is a reference intensity known as the threshold of hearing.
Io = 1 x 10-12 W/m2
This is around the lowest intensity sound we can hear, and it works out to 0 dB. Every 10 dB represents a change of one order of magnitude in intensity. 120 dB, 12 orders of magnitude higher than our reference level, has an intensity of 1 W/m2. Any more intense than this and sounds start getting uncomfortable.
An earthquake measuring 6.0 on the Richter scale is 10 times more powerful as one measuring 5.0, and 1/10th as powerful as one measuring 7.0.
Similarly, a 60 dB sound has ten times the intensity of a 50 dB sound, and 1/10th the intensity of a 70 dB sound.
An increase of x dB means that the sound has increased in intensity by some factor. For instance, any increase by 5 dB represents an increase in intensity by a factor of 3.16.
The decibel equation can also be written in terms of a change. A change in intensity, in dB, is given by:
| Δβ | = (10 dB) * log | ( |
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