http://www.safetyline.wa.gov.au/institute/level2/course18/lecture53/index.asp
The human ear responds to sounds over a very large range of sound intensities:
* the sound intensity of the threshold of hearing (the quietest sound we can hear) is 0.00000000001 watts/m2 (often written 10-12 watts/m2 );
* whilst the sound intensity at the threshold of pain is about 10 watts/m².
DECIBEL SCALE IS USED TO COVER THE RANGE OF SOUND INTENSITIES
To handle this large range we make use of a logarithmic ratio scale called the decibel scale.
In general, a decibel scale for any quantity, q, is defined as:
Lq = 10 log dB (Equation 2.1)
Note that the decibel is not an absolute measure but is referenced to a selected quantity, q ref.
Another reason for using this scale is that the ear itself 'hears' logarithmically and humans judge the relative loudness of two sounds by the ratio of their intensities, a logarithmic behaviour.
The Bel was named after Alexander Graham Bell (1847-1922), the Scottish/American inventor of the telephone and worker for the deaf.
As this unit is rather large it has been divided into ten smaller units called decibels or dB. (deci = one tenth of).
Click here if you want to leave the SafetyLine Institute to take a brief tutorial refresher on logarithms at the University of Wisconsin.
When sound intensity is expressed as a decibel it is referred to as sound intensity level and is given the symbol LI.
To convert sound intensity, I, to sound intensity level LI the following relationship is used:
LI = 10 log dB re Iref (Equation 2.2)
where I = sound intensity whose level is being specified, in watts/m2
and Iref = reference intensity
= 10-12 watts/m2 (the threshold of hearing)
Sound power, W, can also be expressed in decibels and is then referred to as the sound power level, Lw.
Lw = 10 log dB re Wref (Equation 2.3)
where W = sound power of the source in watts
Wref = reference sound power
= 10-12 watts
For sound pressure p, we use the relationship:
Sound pressure level Lp = 10 log = 20 log dB re pref (Equation 2.4)
where p = rms sound pressure in Pa
pref = 2 x 10-5 Pa
(sometimes written as 20 m Pa = 20 x 10-6 Pa, which is the sound pressure at the threshold of hearing at 1000 Hz)
The sound pressure level at the threshold of hearing is thus:
Lp = 20 log = 20 log 1 = 0 dB
