The bel is a logarithmic measure. The number of bels for a given ratio of power levels is calculated by taking the logarithm, to the base 10, of the ratio. Therefore, one bel corresponds to a ratio of 10:1. Mathematically, the number of bels is calculated as B = log_{10}(P _{1}/P _{2}) where P _{1} and P _{2} are power levels. The neper is a similar unit which uses the natural logarithm.
The bel is too large for everyday use, so the decibel (dB), equal to 0.1B, is more commonly used. 1dB is equivalent to a ratio of about 1.259:1. It is defined as 10 log_{10}(P _{1}/P _{2}) where P _{1} and P _{2} are the powers.
The decibel is not an SI unit, although the CIPM[?] has recommended its inclusion in the SI system.

The reason for using the decibel is that the ear is capable of hearing a very large range of sound pressures. The ratio of the sound pressure that causes permanent damage from short exposure to the limit that (undamaged) ears can hear is more than a million. Because the power in a sound wave is proportional to the square of the pressure, the ratio of the maximum power to the minimum power is more than one trillion. To deal with such a range, logarithmic units are useful: the log of a trillion is 12, so this ratio represents a difference of 120 dB.
Psychologists have found that our perception of loudness is roughly logarithmic. In other words, you have to multiply the sound intensity by the same factor to have the same increase in loudness. This is why the numbers around the volume control dial on a typical audio amplifier are related not to the absolute power amplification, but to its logarithm.
Various frequency weightings are used for acoustical measurements to approximate the changes in sensitivity of the ear to different frequencies at different levels. These include the dB(A), dB(B), and dB(C) weightings.
Sounds above 85 decibels are considered harmful, while 120 dB is unsafe and 150 db causes physical damage to the human body. Windows break at 163 db.Jet airplanes are 165 db.Eardums pop at 190 to 198 db. Shock waves and sonic booms are 194 db. Sounds around 200 db can cause death to humans and are generated near bomb explosions. The space shuttle is around 215 db. Nuclear bombs are 240 to 258 db. Even louder are earthquakes, tornados, hurricanes and volcanoes.
In radio electronics, the decibel is used to describe the ratio between two measurements of electrical power. It can also be combined with a suffix to create an absolute unit of electrical power. For example, it can be combined with "m" for "milliwatt" to produce the "dBm". 0 dBm is one milliwatt, and 1dBm is one decibel greater than 0 dBm, or about 1.259 mW.
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