Note! In US the reference 10-13 watts/m2 is commonly used.
Sound Intensity Level can be expressed as:
LI = 10 log (I / Iref)
= 10 log10(I) + 120 (2)
LI = sound intensity level (dB)
I = sound intensity (W/m2)
Iref = 10-12 - reference sound intensity - the threshold of hearing (W/m2)
The logarithmic sound intensity level scale match the human sense of hearing. Doubling the intensity increases the sound level with 3 dB(10 log (2)).
The Decibel Scale
The difference in dB for intensity 10-8 watts/m2 and 10-4 watts/m2 (10000 units) can be calculated as
ΔLI = 10 log ((10-4 watts/m2) / (10-12 watts/m2)) - 10 log (( 10-8 watts/m2) / ( 10-12 watts/m2))
= 40 dB
Increasing the sound intensity by a factor of
Note! Since the sound intensity level may be difficult to measure it is common to use sound pressure level measured in decibels instead. Note that doubling sound pressure raises the sound pressure level with 6 dB.
Sound loudness is a subjective term describing the ear's perception of a sound.
Sound intensity and feeling of loudness:
Sound intensity decreases with the distance to the source. Sound intensity vs. distance can be expressed:
I = N / 4 πr2 (3)
N = sound power (W)
π = 3.14
r = radius or distance from source (m)
The relation between Sound Intensity and Sound Pressure can be expressed as
I = p2 / ρ c (4)
p = sound pressure (Pa)
ρ = density air (1.2 kg/m3 at 20oC)
c = speed of sound (331 m/s)
The relation between Sound Intensity Level and Sound Pressure Level is
LI = Lp - 0.2 (5)
Lp = sound pressure level (dB)
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