# Sound Power, Intensity and Pressure

## An introduction to decibel, sound power, sound intensity and sound pressure

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### The Decibel

Decibel is a logarithmic unit used to describe physical values like the ratio of the signal level - power, sound pressure, voltage or intensity.

The decibel can be expressed as:

decibel = 10 log(P / P_{ref})(1)

where

P= signal power (W)

P_{ref}= reference power (W)

### Sound Power Level

Sound power is the energy rate - the energy of sound per unit of time (J/s, W in SI-units) from a sound source.

Sound power can more practically be expressed as a relation to the threshold of hearing - *10 ^{-12} W* - in a logarithmic scale named Sound Power Level -

*L*

_{w}:

L_{w}= 10 log (N / N_{o})(2)

where

L_{w}= Sound Power Level in Decibel (dB)

N= sound power (W)

- The lowest sound level that people of excellent hearing can discern has an acoustic sound power about 10
^{-12}W, 0 dB - The loudest sound generally encountered is that of a jet aircraft with a sound power of 10
^{5}W, 170 dB.

### Sound Intensity

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

The Sound Intensity Level can be expressed as:

L_{I}= 10 log(I / I_{ref})(3)

where

L_{I}= sound intensity level (dB)

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

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

### Sound Pressure Level

The Sound Pressure is the force (N) of sound on a surface area (m^{2}) perpendicular to the direction of the sound. The SI-units for the Sound Pressure are N/m^{2} or Pa.

The Sound Pressure Level:

L_{p}= 10 log(p^{2}/ p_{ref}^{2}) = 10 log(p / p_{ref})^{2}= 20 log (p / p_{ref})(4)

where

L_{p}= sound pressure level (dB)

p= sound pressure (Pa)

p_{ref}= 2 10^{-5}- reference sound pressure (Pa)

- If the pressure is doubled, the sound pressure level is increased with
*6 dB (20 log (2))*

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