SPL summation

Decibels do not add like ordinary numbers.

Convert each level back to a linear energy ratio, add the energies, then convert back to decibels. Perfectly in-phase coherent signals instead add in pressure amplitude.

The formula

• $L_1, L_2$ — source levels in $\text{dB}$
• For in-phase sources, replace $10$ with $20$

Worth knowing

Two equal uncorrelated sources add 3 dB. Two equal, perfectly in-phase sources add 6 dB. A source more than 10 dB quieter adds less than half a decibel in uncorrelated mode.

Assumptions

Real loudspeakers carrying the same signal create frequency-dependent interference. Neither mode predicts an entire room; measure at multiple listening positions.

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