Decibel is a logarithmic unit used to describe the ratio of a signal level - like power, sound pressure, voltage, intensity etc. to a reference level
The decibel is a logarithmic unit used to describe the ratio of a signal level - like power, sound pressure, voltage, intensity etc. - to a reference level.
- the decibel express the level of a value relative to a reference value
The decibel level of a signal can be expressed as
L = 10 log (S / Sref) (1)
L = signal level (decibel, dB)
S = signal (signal unit)
Sref = reference signal (signal unit)
Decibel is a dimensionless value of relative ratios. The signal units depends on the nature of the signal - can be W for power, Pa for pressure and so on.
A decibel is one-tenth of a Bel - named after Alexander Graham Bell, the inventor of the telephone.
Note! - the decibel value of a signal increases with 3 dB if the signal is doubled (L = 10 log (2) = 3).
If the decibel value and reference level are known the absolute signal level can be calculated by transforming (1) to
S = Sref 10(L / 10) (2)
S - signal (signal unit)
Sref - reference signal (signal unit)
Example - Lowest Hearable Sound Power
10-12 W is normally the lowest sound power possible to hear and this value is normally used as the reference power for sound power calculations.
The sound power in decibel from a source with the lowest sound hearable can be calculated as
L = 10 log ((10-12 W) / (10-12 W))
= 0 dB
Example - Highest Hearable Sound Power
100 W is almost the highest sound power possible to hear. The sound power in decibel from a source with the highest possible to hear sound power can be calculated as
L = 10 log ((100 W) / (10-12 W))
= 140 dB
Example - Sound Power from a Fan
A fan creates 1 W of sound power. The noise level from the fan in decibel can be calculated as
L = 10 log ((1 W) / (10-12 W))
= 120 dB
Example - Sound Intensity and Decibel
The difference in decibel between sound intensity 10-8 W/m2 and sound intensity 10-4 W/m2 (10000 units) can be calculated as
ΔL = 10 log ((10-4 W/m2) / (10-12 W/m2)) - 10 log ((10-8 W/m2) / (10-12 W/m2))
= 40 dB
Increasing the sound intensity by a factor of
- 10 raises its level by 10 dB
- 100 raises its level by 20 dB
- 1000 raises its level by 30 dB
- 10000 raises its level by 40 dB and so on