Adding uncorrelated sound sources raises level as the square root of their number

Evidence

On the other hand, if the sound waves are uncorrelated, then they do not add algebraically, like correlated waves; instead, we must add the powers of the individual waves together. As stated earlier, the power in a waveform is proportional to the square of the pressure levels, so in order to sum the powers of the waves, we must square the pressure amplitudes before adding them together. If we want the result as a pressure, then we must take the square root of the result. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 244 (#expands, via linked claim)

Categorization

• XREF: connects to: Adding equal sound intensities yields a 3 dB total increment; Decibel increases map powers of ten to logarithms; Correlated sound sources add pressures while uncorrelated ones add energy (+6 more)

Broader Connections

• Uncorrelated sound waves sum by power, not by amplitude. #expands (0.90) — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 244
• Uncorrelated source totals ignore the relative phases of signals. #corroborates (0.85)
• The power spectrum is blind to the relative phase of a sound’s components #corroborates (0.80)
• Correlated sound sources create spatial interference patterns that uncorrelated sources do not. #complicates (0.75)