# Decibel

The human ear responds logarithmically and it is convenient to deal in logarithmic units in audio systems. The bel is the logarithm of the ratio of two powers, and the decibel is one tenth of a bel.

The Bel was the amount a signal dropped in level over a one-mile distance of telephone wire.

The decibel scale is often used to express the signal to noise ratio, frequency and amplitude response limits in the majority of instrument specifications. The main application is, however, in the acoustic field to define response limits in audio equipment and as a means of defining noise levels. In the latter case a sound pressure level is defined in decibels in which case a reference pressure of 2x10-5Pa is used as a base pressure and the pressure measured by a microphone is related to this standard base pressure.

The logarithmic nature of the decibel allows us to compare two values of enormously different magnitudes with conveniently small numbers. e. g. the limits of hearing in terms of absolute pressure level cover the range from 20µPa to 200,000,000 µPa. The same range expressed in dB SPL is 0 -140 dB SPL. This is much more convenient.

A difference of 20 dB between two sounds means that the more intense one has 10 times the amplitude (100 times the power) of the softer. A change of 3dB is commonly thought to be the smallest change in sound pressure level that can be remembered.

Note: whenever quoting any level as a dB care should be taken to specify the reference level. In acoustics this is often dropped.

 Acceleration level
 Velocity level
 Force level
 Power level
 Intensity level
 Energy Density level
 Energy level

Acousticians use the dB scale for the following reasons:

• Quantities of interest often exhibit such huge ranges of variation that a dB scale is more convenient than a linear scale. For example, sound pressure radiated by a submarine may vary by eight orders of magnitude depending on direction.
• The human ear interprets loudness on a scale much closer to a logarithmic scale than a linear scale.

In all cases, one decibel equals about 0.115129 neper and d decibels equal d(ln 10)/20 nepers.

See also: dB FS, dBA, dBB, dBc, dBi, dBLi, dBm, dBrn, dBsm, dBu, dBv, dBW, dBZ, Logarithm, Mel.