Decibel Addition & Subtraction
Combine incoherent sound sources energetically, or strip background noise out of a measurement.
Inputs
Why decibels don't add arithmetically
A decibel is a logarithmic ratio of energy-like quantities (intensity, power, mean-square pressure). Two uncorrelated sources add their energies, not their decibel numbers, so each level must be converted back to a linear quantity, summed, then converted again:
This yields the well-known rules of thumb that the addition chart on this page visualises:
- Two equal sources: +3 dB (double the energy).
- Ten equal sources: +10 dB.
- A source 10 dB quieter than another adds only 0.4 dB; at 20 dB difference it is negligible (0.04 dB).
Energy average
The energy-mean level is L_\mathrm{total} - 10\cdot\log_{10}(n). It is always higher than the arithmetic mean because loud samples dominate. This is the same principle behind L_\mathrm{eq}.
Background-noise correction
When the source cannot be measured alone, measure the total and then the background with the source switched off. The source level is recovered by energetic subtraction:
Standards such as ISO 3744 require a difference of at least 6 dB (preferably more than 10 dB). Below 3 dB the correction becomes larger than the uncertainty of the measurement itself and the result is unreliable.
Assumptions
Sources must be incoherent (uncorrelated). Two coherent tones of identical frequency can interfere, giving anything from total cancellation to +6 dB.