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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 or intensity - to a reference level.

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

Decibel Definition

The decibel level of a signal can be expressed as

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

where

L = signal level (decibel, dB)

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

Sref = 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).

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)

Decibel Calculator

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

Sref - reference signal - intensity or power level (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 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/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

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

The relative scale of objects.

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

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9.19.12
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