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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 10⁵ 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/m². 

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/m²)

I_ref = 10^-12 - reference sound intensity (W/m²) 

Sound Pressure Level

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

The Sound Pressure Level: 

L_p = 10 log( p² / p_ref² ) = 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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