# Decibel

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 | Power Ratio (S/S _{ref}) | Amplitude Ratio (A/A_{ref}) |
---|---|---|

-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)

### Decibel Calculator

### 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

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

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The rules of logarithms - log_{10} and log_{e} for numbers ranging 1 to 1000.

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### Outdoor Ambient Sound Pressure Levels

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### 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

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### Sound Intensity

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### 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.