Question 73794
The loudness of sound is based on intensity level measured in decibels using a logarithmic scale and is relative to (a ratio of) the weakest sound the ear can hear.
:
With sound intensity we can use the decibel formula which compares a sound to
the threshold of hearing which is given as 10^-12. (Io in the formula)
:
D = 10*log(I/Io)
where:
D = level of  sound in decibels 
I is the sound intensity measured in watts per square meter
Io is the threshold of hearing, which I is to be compared with (usually)
:
Here are some intensity examples, I got out of an old algebra book:
1*(10^-12) Threshold of hearing
5.2(10^-10) Whisper
3.2(10^6) Normal conversation, (ahh, but what is normal??)
8.5(10^-4) Heavy traffic
3.2(10^-3) Jackhammer
1*(10^0) Threshold of pain
8.3(10^2) Jet plane with afterburner

:
An example
Normal conversation is given as I = 3.2(10^-6): Find the Decibel level
D = 10*log{{{(3.2*10^-6)/(10^-12)}}}
:
D = 10*log(3.2*10^6): Remember 10^-6 divided by 10^-12 = 10^+6
:
D = 10(6.50515); Enter: log(3.2*10^6) on a good calculator)
:
D = 65 decibels is the level of normal conversation
:
Try using this method to find the decibel of a whisper, you should get about
27 decibels
:
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The reason they use a logarithmic scale is because the ear has an incredible
hearing range. The loudest a healthy person can hear is about a trillion times
the softest sound it can hear. Logs makes comparing these levels manageable.
:
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