# Sound Power -, Intensity - and Pressure Level

## 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 ratios of physical values like - like power, sound pressure, voltage, intensity and more.

The decibel can be expressed as:

L = 10 log (S / S_{ref})(1)

where

L = signal level (dB)

S= signal (signal unit)

S_{ref}= signal reference (signal unit)

### 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 in a logarithmic scale named Sound Power Level as the ratio of sound power to the sound power at the threshold of hearing - *10 ^{-12} W*

*:*

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

where

L_{N}= Sound Power Level (decibel , dB)

N= sound power (W)

N_{ref}= reference sound power (10^{-12}W)

- The lowest sound power persons with excellent hearing can discern is about
*10*- defined as^{-12}W*0 dB*in the decibel scale - The loudest sound power generally possible to encounter is that of a jet aircraft with a sound power of
*10*-^{5}W*170 dB*

### Sound Intensity Level

Sound intensity is the ratio acoustic or sound power to area. The SI-unit for Sound Intensity is *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 a sound on a surface area *(m ^{2})* perpendicular to the direction of the sound. The SI-unit for the Sound Pressure is

*N/m*.

^{2}or PaThe Sound Pressure Level in decibel can be expressed as

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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