# Difference between revisions of "Bel"

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− | + | The '''bel''' is a logarithmical unit used to express relative difference in intensity or power between two signals, usually acoustic. Because of the fact that the Bel unit is too large for everyday use most of the times it is used as the more convenient '''decibel''' (abbreviated to '''dB'''). | |

− | + | Decibel is equal to ten times the common logarithm of the ratio of the two levels. | |

− | + | ::<math>{di\! f\!\! f} = \cdot \log_{10}\left(\frac{P_2}{P_1}\right )</math> | |

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+ | In case of the decibel we have a ''10'' factor: | ||

::<math>{di\! f\!\! f} = 10 \cdot \log_{10}\left(\frac{P_2}{P_1}\right )</math> | ::<math>{di\! f\!\! f} = 10 \cdot \log_{10}\left(\frac{P_2}{P_1}\right )</math> | ||

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There is a second definition of the decibel. In acoustics, it is used to express the ratio in sound pressure, because power is roughly proportional to the square of effective sound pressure. | There is a second definition of the decibel. In acoustics, it is used to express the ratio in sound pressure, because power is roughly proportional to the square of effective sound pressure. | ||

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Let 'p' be pressure, 'P' power. | Let 'p' be pressure, 'P' power. | ||

− | ::<math>{di\! f\!\! f} = | + | ::<math>{di\! f\!\! f} = \cdot \log_{10}\left(\frac{P_2}{P_1}\right )</math> |

− | ::<math>{di\! f\!\! f} = | + | ::<math>{di\! f\!\! f} = \cdot \log_{10}\left(\frac{p_2^2}{p_1^2}\right )</math> |

− | ::<math>{di\! f\!\! f} = | + | ::<math>{di\! f\!\! f} = 2 \cdot \log_{10}\left(\frac{p_2}{p_1}\right )</math> because <math>\log_{10}(a^2) = 2 \cdot \log_{10}(a)</math> |

In this scale, it means an increase of 20 dB is equal to a ten-fold ratio, or 6 dB a two-fold ratio (<math>20 \cdot \log_{10}(2)</math> ''is approximately equal to 6''). | In this scale, it means an increase of 20 dB is equal to a ten-fold ratio, or 6 dB a two-fold ratio (<math>20 \cdot \log_{10}(2)</math> ''is approximately equal to 6''). | ||

[[Category:Technical]] | [[Category:Technical]] |

## Revision as of 18:33, 14 June 2007

The **bel** is a logarithmical unit used to express relative difference in intensity or power between two signals, usually acoustic. Because of the fact that the Bel unit is too large for everyday use most of the times it is used as the more convenient **decibel** (abbreviated to **dB**).

Decibel is equal to ten times the common logarithm of the ratio of the two levels.

In case of the decibel we have a *10* factor:

There is a second definition of the decibel. In acoustics, it is used to express the ratio in sound pressure, because power is roughly proportional to the square of effective sound pressure.

Let 'p' be pressure, 'P' power.

- because

In this scale, it means an increase of 20 dB is equal to a ten-fold ratio, or 6 dB a two-fold ratio ( *is approximately equal to 6*).