Coherent sound addition yields double the amplitude gain of incoherent addition

Evidence

When two coherent signals with the same amplitude A are added constructively, the resulting signal has the amplitude 2A, which means an increase in level of 20 log10(2A/A) ≈6 dB. If two incoherent signals with the same amplitude are added, the resulting level will increase by 10 log10(2A2/A2) ≈3 dB. — Ville Pulkki, Matti Karjalainen, Communication Acoustics- An…, 217

Categorization

• XREF: The 6 dB vs 3 dB coherent/incoherent addition rule is the foundation behind speaker array design and comb-filtering artifacts in audio engineering.