What is the decibel formula?

Answer 1

The decibel, or dB, is a means of expressing the gain of an active device (such as an amplifier) or the loss in a passive device (such as an attenuator or length of cable). It is simply the ratio (!) of output to input expressed in logarithmic form. The decibel was developed by the telephone company to express the gain or loss in telephone transmission systems.

Sound intensity (sound energy quantity):

Reference sound intensity Io = 10^−12 W/m² (Threshold of hearing)

Reference sound intensity level LIo = 0 dB-SIL (Threshold of hearing level)

Get sound intensity I when entering sound intensity level LI:

Sound intensity I = Io×10^(LI/10) W/m² = 10^−12×10^(LI/10) W/m².

Get sound intensity level LI in dB when entering sound intensity I in W/m²:

Sound intensity level LI = 10×log (I / Io) dB = 10×log (I / 10^−12) dB.

Sound pressure (sound field quantity):

Reference sound pressure po = 20 µPa = 2×10^−5 Pa (Threshold of hearing)

Reference sound pressure level Lpo = 0 dB-SPL (Threshold of hearing level)

Get sound pressure p when entering sound pressure level Lp:

Sound pressure p = po×10^(Lp/20) Pa or N/m² = 2×10^−5×10^(Lp/20) Pa.

Get sound pressure level Lp in dB when entering sound pressure p in Pa:

Sound pressure level Lp = 20×log (p / po) dB = 20×log (p / 2×10^−5) dB.