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# Decibel

## Logarithmic unit used to describe ratios of signal levels - like power or intensity - to a reference level.

The decibel is a logarithmic unit used to describe the ratio of a signal level - like power, intensity or amplitude - to a reference level.

• the decibel express the level of a value relative to a reference value

Two types of decibel are normally used:

• for power ratios - dB is defined as ten times the logarithm in base 10
• for amplitude ratios - root power quantities - a change in amplitude by a factor of 10 corresponds to 20 dB change in level

### Decibel Definition - Power Ratios

The decibel level of a signal can be expressed as

L = 10 log (S / S ref)                (1)

where

L = signal level (decibel, dB)

S = signal - intensity or power level (signal unit)

S ref = reference signal - intensity or power level (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.

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).

dB vs. Signal Ratio
dBPower Ratio
(S/Sref)
Amplitude Ratio (A/Aref)
-40 0.0001 0.01
-20 0.01 0.1
0 1 1
3 2 √2
6 4 2
10 10 3.162
20 100 10

If the decibel value and reference level are known the absolute signal level can be calculated by transforming (1) to

S = S ref 10 (L / 10)                                                       (2)

### 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 in 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/m 2 and sound intensity 10 -4 W/m 2 ( 10000 units) can be calculated as

ΔL = 10 log ((10 -4 W/m 2) / (10 -12 W/m 2)) - 10 log ((10 -8 W/m 2) / (10 -12 W/m 2))

= 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

### Decibel Ratios - Amplitude Ratios

L = 20 log (A / A ref)                (3)

where

L = signal level (decibel, dB)

A = amplitude level (signal unit)

A ref = amplitude level level (signal unit)

## Related Topics

• ### Acoustics

Room acoustics and acoustic properties. decibel A, B and C calculations. Noise Rating (NR) curves. Sound transmission through walls. Calculate sound pressure, sound intensity and sound attenuation.
• ### Miscellaneous

Engineering related topics like Beaufort Wind Scale, CE-marking, drawing standards and more.
• ### Noise and Attenuation

Noise is usually defined as unwanted sound - noise, noise generation, silencers and attenuation in HVAC systems.

## Related Documents

• ### Decibel A, B and C

Sound pressure filters that compensates for the hearing sensed by the human ear.
• ### Logarithms

The rules of logarithms - log10 and loge for numbers ranging 1 to 1000.
• ### Maximum Sound Pressure Levels in Rooms

Maximum recommended sound pressure levels in rooms like kindergartens, auditoriums, libraries, cinemas and more.
• ### Noise generated in Air Ducts

Estimate noise generated by air flow in ducts.
• ### Outdoor Ambient Sound Pressure Levels

Outdoor ambient sound pressure levels (dBA) in rural and urban business and industrial environments with or without limited traffic.
• ### Phonetic Alphabet

The phonetic alphabet used in international aircraft communications.
• ### Scales of Objects

The relative scale of objects.
• ### Signals - Adding Decibels

The logarithmic decibel scale is convenient when adding signal values like sound power, pressure and others from two or more sources.
• ### SIL - the Speech Interference Levels

Background noise frequencies that interferes with speech.
• ### Sound Intensity

Acoustic power of sound per unit area.
• ### Sound Intensity, Power and Pressure Levels

Introduction to decibel, sound power, intensity and pressure.
• ### Sound Pressure

Sound Pressure is the force of sound on a surface perpendicular to the propagation of sound.
• ### Use of Telephones in Noisy Areas

Satisfactory, difficult and impossible noise levels for telephone use in noisy areas.

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## Citation

• The Engineering ToolBox (2003). Decibel. [online] Available at: https://www.engineeringtoolbox.com/decibel-d_341.html [Accessed Day Month Year].

Modify the access date according your visit.

6.3.17

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