Sound Intensity is the Acoustic or Sound Power (W) per unit area. The SI-units for Sound Intensity are W/m2.
The dynamic range of human hearing and sound intensity spans from 10-12 W/m2 to
10 - 100 W/m2. The highest sound
intensity possible to hear is 10,000,000,000,000 times as loud as the
This span makes the absolute value of the sound intensity impractical for normal use. A more convenient way to express the sound intensity is the relative logarithmic scale with reference to the lowest human hearable sound - 10-12 W/m2 (0 dB).
Note! In US a reference of 10-13 watts/m2 are commonly used.
The Sound Intensity Level can be expressed as:
LI = 10 log(I / Iref) (1)
LI = sound intensity level (dB)
I = sound intensity (W/m2)
Iref = 10-12 - reference sound intensity (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 difference in intensity of 10-8 watts/m2 and 10-4 watts/m2 (10,000 units) can be calculated in decibels 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. Doubling the Sound Pressure raises the Sound Pressure Level with 6 dB.
Sound intensity and feeling of loudness:
The sound intensity decreases with distance to source. Intensity and distance can be expressed as:
I = Lw / 4 π r2 (2)
Lw = sound power (W)
π = 3.14
r = radius or distance from source (m)
The connection between Sound Intensity and Sound Pressure can be expressed as:
I = p2 / ρ c (3)
p = sound pressure (Pa)
ρ = density of air (1.2 kg/m3 at 20oC)
c = speed of sound (331 m/s)