Decibels

The decibel (dB) is a unit named after Alexander Graham Bell, known as a telecommunications pioneer. A decibel is defined as one tenth of a bel, i.e., to convert from Bel to dB you multiply by 10:

$$1$$    B$$= 10$$    dB$$$$

The decibel is a logarithmic scale, used to compare two quantities such as the power gain of an amplifier or the relative power of two sound sources. The decibel difference between two power levels $\Delta L$ for example, is defined in terms of their power ratio $W_2/W_1$ and is given in decibels by:

$$\Delta L = 10\log W_2/W_1$$   dB$$.$$

Since power is proportional to intensity, the ratio of two signals with intensities $I_1$ and $I_2$ is similarly given in decibels by

$$\Delta L = 10\log I_2/I_1$$   dB$$.$$