Combining sound levels combine sound levels two sources resultant level non-coherent uncorrelated sound sources signals decibels or SPL signals add signal noise levels non-coherent incoherent - sengpielaudio
 
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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.
 
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.

 
Sum calculation of two non-coherent signals - "Acoustic level addition"
 
1st sound source
 Level
L1:  dB 
  |
  |
  |
  |
 
+ 2nd sound source
 Level
L2:   dB 
  |
  |
  |
  |
 Total level from 
 both sources: 
  =   dB
 
   Non-coherent signals!      
"Power sum"
90° - non-coherent            0° - coherent
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:
Formula non-coherent signals
 
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:
Formula coherent signals
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

Combined Sound Pressure Levels - sengpielaudio
 
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

Source 1  dB                 
Source 2  dB
Source 3  dB
Source 4  dB
 Total sum  dB
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?

Regenbogenlinie

Adding of equal loud non-coherent sound sources

Level adding
Level increase Δ L for
n equal loud sound sources
Number of n equal loud sound sources

Level increase
Δ L in dB

  1
  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.

Equal strong non-coherent sound sources
Number of sound sources n:
 
 ↔  Increase of level Δ L:
dB
Formula 1   Formula 2
 

The total level in dB is the level of one sound source plus the increase of level in dB.
 
Formula sum of non-coherent sources 2

See also:
Adding decibels of one-third octave bands to level of octave band
Combining decibels - adding up to thirty acoustic sound levels

 
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