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Sound level in decibels

The ear perceives sound over an enormous range of intensities, so sound level is measured on a logarithmic scale in decibels. An increase of 10 dB means ten times the intensity, and three decibels more means roughly double the intensity.

L = 10\lg\frac{I}{I_0}

sound level

I_0 = 10^{-12}\ \tfrac{W}{m^2}

threshold of hearing

Symbols

$L$	sound level	dB
$I$	intensity	W/m²
$I_0$	reference intensity	W/m²

Example

Two identical machines at 80 dB each:

$10\lg(2\cdot 10^8) \approx 83$ dB, not 160 dB.

Decibels cannot be added directly. Convert to intensity first.

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Part of Foundations of Physics: Waves, sound and light.