Total dB level adding of non-coherent incoherent uncorrelated sound sources signals combine sound levels two sources resultant level decibels or SPL sound pressure level add signal noise levels non-coherent incoherent random phase acoustic

Sound calculations
● Total level adding of non-coherent sound sources ●
Fact: Power sum or Power addition

Adding the level of two uncorrelated (non-coherent) sound sources,
Combining acoustical levels of e.g. a violin and a violoncello
as sound power sum (total sound power).
For beginners: non-coherent or incoherent (random phase) means that the signals of the channels are irrelative
like a violin and a cello having no correlative relationship. Often we say uncorrelated when we mean incoherent.

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Decibels are logarithmic "units", they may not be added linearly like other figures.
In most cases we will add uncorrelated signals as noise or music. If a sound source creates a sound level (SPL) of L₁ = 60 dB and another source with L₂ = 60 dB is added, then it is not the level of 120 dB, but gives a non-coherent summing of the signal level of 63 dB. If both values are equal, it is easy.
More than 3 dB greater than the higher of the two non-coherent levels is not possible for the total sum in decibels. See also the other case:
● Total level adding of electrical coherent signals.


Power summing non-coherent (90°) √ (1² + 1²) = 1,414...		Voltage summing coherent (0°) 1 + 1 = 2

Adding of two non-coherent (incoherent) sound pressure levels or voltage levels:

Adding of two values of the same level results an increase of the total level of (+)3 dB.
This equation is used for electrical adding of non-coherent signals, and for the calculation of the energy level of two loudspeakers.

Adding of two coherent sound pressure levels or voltage levels:

Adding of two values of the same level results an increase of the total level of (+)6 dB.
This is obtained by feeding two side-by-side loudspeakers with the same signal.

Combined Sound Pressure Levels - sengpielaudio

Level difference between the two sound sources

Adding of two different acoustical levels

For the sound level of n non-coherent radiating sound sources we get:
SPL Addition 01

p₀ is the reference value of the sound pressure. Auditory threshold at 1 kHz = 0.00002 Pa = 20 µPa.

Level adding of up to four sound sources

Adding decibels - combining up to ten acoustic levels
Combining decibels of one-third octave bands to level of octave band and vice versa
How many decibels (dB) sound level change is twice (double, half) or three times as loud?
Damping of sound level with distance
How does the sound decrease with distance?
How do Sound Pressure Levels add when listening?
What is an Amplitude?

Adding of equal loud non-coherent sound sources

Level increase Δ L for n equal loud sound sources
Number of n equal loud sound sources	Level increase Δ L in dB
1	0
2	3.0
3	4.8
4	6.0
5	7.0
6	7.8
7	8.5
8	9.0
9	9.5
10	10.0
12	10.8
16	12.0
20	13.0

Formulas: Δ L = 10 × log n or n = 10^(ΔL/10)
Δ L = level difference; n = number of equal loud sound sources.

n = 2 equally loud non-coherent sound sources result in a higher level of
10 × log₁₀ 2 = +3.01 dB compared to the case that only one source is available.
n = 3 equally loud non-coherent sound sources result in a higher level of
10 × log₁₀ 3 = +4.77 dB compared to the case that only one source is available.
n = 4 equally loud non-coherent sound sources result in a higher level of
10 × log₁₀ 4 = +6.02 dB compared to the case that only one source is available.
n =10 equally loud non-coherent sound sources result in a higher level of
10 × log₁₀ 10 = +10.00 dB compared to the case that only one source is available.

Adding (combining) levels of equal loud sound sources

Simply enter the value to the left or the right side.
The calculator works in both directions of the ↔ sign.

The total level in dB is the level of one sound source plus the increase of level in dB.

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Equal strong non-coherent sound sources
Number of sound sources n:	↔	Increase of level Δ L: dB