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# Sound Intensity, Power and Pressure Levels

## Introduction to decibel, sound power, sound intensity and sound pressure

### 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 / Sref)                                        (1)

where

L = signal level (dB)

S = signal (signal unit)

Sref = 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:

LN = 10 log (N / Nref)                                   (2)

where

LN = Sound Power Level (decibel , dB)

N = sound power (W)

Nref = reference sound power (10-12 W)

• The lowest sound power persons with excellent hearing can discern is about 10-12 W -  defined as 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 105 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/m2

The Sound Intensity Level can be expressed as:

LI = 10 log (I / Iref)                                (3)

where

LI = sound intensity level (dB)

I = sound intensity (W/m2)

Iref = 10-12 - reference sound intensity (W/m2

### Sound Pressure Level

The sound pressure is the force (N) of a sound on a surface area (m2) perpendicular to the direction of the sound. The SI-unit for the Sound Pressure is N/m2 or Pa.

The Sound Pressure Level in decibel can be expressed as

Lp = 10 log (p2 / pref2)

= 10 log (p / pref)2

= 20 log (p / pref)                                  (4)

where

Lp = sound pressure level (dB)

p = sound pressure (Pa)

pref = 2 10-5 - reference sound pressure (Pa)

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

## Related Topics

• Acoustics - Room acoustics and acoustic properties - decibel A, B and C - Noise Rating (NR) curves, sound transmission, sound pressure, sound intensity and sound attenuation
• Physiology - Human physiology, air quality and comfort temperatures, activity and metabolic rates, health effects of carbon monoxide and more
• Noise and Attenuation - Noise is usually defined as unwanted sound - noise, noise generation, silencers and attenuation in HVAC systems

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