One of the most frequent applications of the decibel scale is in the communication and entertainment industries. The human ear responds in a logarithmic fashion to changes in audio power levels.
To establish a basis for comparison between audio levels, a reference level of \(20\) micropascals (\(\mu\textrm{Pa}\)) was chosen. The \(20\;\mu\textrm{Pa}\) level is the threshold level of hearing (\(0\;\textrm{dB}\)). Using this reference level, the sound pressure level in decibels is defined by the following equation:
\(\boxed{\mathrm{dB}_s = 20\log_{10}\left(\frac{P}{20\;\mu\textrm{Pa}}\right)}\quad\textrm{dB}\)
where \(P\) is the sound pressure in micropascals (\(\mu\textrm{Pa}\)).
To double the sound level received by the human ear, the power rating of the acoustical source (in watts) must be increased by a factor of 10.
At normal hearing levels, it would take a change of about \(3\;\textrm{dB}\) (twice the power level) for the change to be noticeable to the human ear.
At low levels of sound, a change of \(2\;\textrm{dB}\) may be noticeable, but it may take a \(6\;\textrm{dB}\) (four times the power level) change for much higher levels of sound.