Decibels

• The decibel is defined as one tenth of a bel which is named after Alexander Graham Bell, the inventor of the telephone.
• 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$$.$$