# Sound Intensity

## The sound intensity level is the acoustic power of a sound per unit of area in relation to a fixed reference

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### Sound Intensity

Sound Intensity is the Acoustic or Sound Power *(W)* per unit area. The SI-units for Sound Intensity are *W/m ^{2}*.

### Sound Intensity Level

The dynamic range of human hearing and sound intensity spans from *10 ^{-12} W/m^{2}* to

*10 - 100 W/m*. The highest sound intensity possible to hear is

^{2}*10,000,000,000,000*times as loud as the quietest!

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/m^{2 }

*(0 dB)*.

**Note!** In US a reference of *10 ^{-13} watts/m^{2}* are commonly used.

The Sound Intensity Level can be expressed as:

L_{I}= 10 log(I / I_{ref})(1)

where

L_{I}= sound intensity level (dB)

I= sound intensity (W/m^{2})

I_{ref}= 10^{-12}- reference sound intensity (W/m^{2})

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))*.

### Example - Sound Intensity

The difference in intensity of *10 ^{-8} watts/m^{2} *and

*10*(

^{-4}watts/m^{2}*10,000 units*) can be calculated in decibels as

ΔL_{I}= 10 log((10^{-4}watts/m^{2}) / (10^{-12}watts/m^{2}))

- 10 log(( 10^{-8}watts/m^{2}) / ( 10^{-12}watts/m^{2}))

= 40 dB

Increasing the sound intensity by a factor of

*10 raises its level by 10 dB**100 raises its level by 20 dB**1,000 raises its level by 30 dB**10,000 raises its level by 40 dB**and so on*

**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*.

### Loudness

Sound loudness is a subjective term describing the strength of the ear's perception of a sound.

Sound intensity and feeling of loudness:

*110 to 225 dB - Deafening**90 to 100 dB - Very Loud**70 to 80 dB - Loud**45 to 60 dB - Moderate**30 to 40 dB - Faint**0 - 20 dB - Very Faint*

### Sound Power, Intensity and Distance to Source

The sound intensity decreases with distance to source. Intensity and distance can be expressed as:

I = L_{w}/ 4 πr^{2 }(2)

where

L_{w}= sound power (W)

π= 3.14

r= radius or distance from source (m)

### Sound Intensity and Sound Pressure

The connection between Sound Intensity and Sound Pressure can be expressed as:

I = p^{2}/ ρ c(3)

where

p= sound pressure (Pa)

ρ= density of air (1.2 kg/m^{3}at 20^{o}C)

c= speed of sound (331 m/s)

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