Total dB level adding of coherent correlated acoustical sound sources signals combining decibels or SPL sound pressure level audio logarithmic decibel scale loudspeaker add signal incoherent noncoherent - sengpielaudio
 
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Total level adding of coherent signals 
Fact: Voltage sum or Voltage addition
 
Adding the level of two steady correlated (in phase) sources
Coherent Signal Summing: This results from the fact that the sum voltage
will be twice the voltage of a single signal.

 
Decibels are logarithmic "units" that can not be added to other numbers linearly. If a source creates a level L1 and a second source L2 that is built from the first, (as two closely powered loudspeakers get the same signal), then this gives a sum of the level which is 6 dB higher than the level of one signal.
If both values are the same level, that's easy. The situation changes when both steady correlated or coherent combined levels are different. More than 6 dB higher than the higher of the two levels of the coherent sum level can never be reached.
Note: This calculation here should not be confused with the usual addition of two acoustic "incoherent" (noncoherent) sources - such as a violin and a trumpet. See also the other case:

● Total level adding of acoustical incoherent (noncoherent) sound sources.

 
Sum calculation of two coherent signals - "Electric level addition"

1st source
 Level L1  dB 
  |  
  |  
  |  
  |  

+ 2nd source
 Level L2  dB 
  |  
  |  
  |  
  |  
 Total level of
  both sources 
  =  dB
 
  Coherent signals!      
"Voltage sum"

Adding amplitudes (and levels)

0° - coherent            90° - incoherent
Voltage sum
coherent (0°)
1 + 1 = 2
  Power sum
incoherent (90°)
√ (1² + 1²) = 1,414...
 
Adding of two coherent pressure or voltage level:
Formula coherent signals
Adding of two values of the same level results in an increase in the overall level here of (+) 6 dB.
This is obtained with the equal input of two closely standing speakers.

 
Adding of two incoherent (noncoherent) pressure or voltage level:
Formula incoherent signals
Adding of two values of the same level results in an increase of the total level of (+) 3 dB.
This equation is used for both the electric incoherent addition of signals, and for the calculation
of the energy level of two loudspeakers.

Level addition of several coherent signals

 
source 1  dB                 
source 2  dB
source 3  dB
source 4  dB
total sum  dB
 
Total level adding of incoherent sources
Amplitude sum and squared total amplitude in dB
How do Sound Pressure Levels add when listening?
What is amplitude?

Regenbogenlinie

Adding of equal strong coherent signals

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

 Level increase 
Δ L in dB

  1
  2   6.0
  3   9.6
  4   12.0
  5   14.0
  6   15.6
  7   17.0
  8   18.0
  9   19.0
10   20.0
12   21.6
16   24.0
20   26.0

Formulas: Δ L = 20 × log n  or  n = 10(ΔL/20)
Δ L = level difference; n = number of equal coherent sources.

n = 2 coherent sources of equal level result in a higher level of
20 × log10 2 = +6.02 dB compared to the case that only one source is available.

n = 3 coherent sources of equal level result in a higher level of
20 × log10 3 = +9.54 dB compared to the case that only one source is available.

n = 4 coherent sources of equal level result in a higher level of
20 × log10 4 = +12.04 dB compared to the case that only one source is available.

n = 10 coherent sources of equal level result in a higher level of
20 × log10 10 = +20.00 dB compared to the case that only one source is available.

Adding (combining) equal strong coherent sources

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

Adding equal strong coherent sources
Number of sound sources n
 
 ↔  Increase of level Δ L
dB
Formula1   Formula2
 

The total level in dB is the level of one source plus the increase of level in dB.
Formula: Sum of 2 coherent sources

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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