Combining sound levels - combining decibels or SPL of incoherent sound sources add signal noise levels - sengpielaudio
 
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Total Level Calculation

Adding the level of two uncorreleted (incoherent)
sound sources, like e.g. a violin and a violoncello

Total level  adding of two incoherent sources

For beginners: incoherent means the signals of the two channels are irrelative like a violin and a cello,
that means having no correlative relationship. Sometimes we say uncorrelated when we mean incoherent.


Decibels are logarithmic "units", they may not be added linearly like other figures.
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 summing
level of 63 dB. If both values are equal, it is easy. More than 3 dB greater than the
higher of the two levels is not possible for the total sum in dB.

1st sound source
Level L1: dB 

2nd sound source
 Level L2: dB 

Total level from
both sound sources: 
dB
 
     

Level difference in dB of the levels
Addieren der Pegel zweier inkohärenter Schallquellen - sengpielaudio
The level difference which has to be added to the higher of the two levels

Adding of two levels

Pegelzunahme zweier Schallquellen - sengpielaudio

                 Level difference between the two sound sources

For the sound pressure level of n incoherent radiating sound sources we get:
SPL Addition 01

p0 is the reference value of the soundpressure. Auditory threshold at 1 kHz = 0.0002 Pa.

Adding of two incoherent sound pressure levels or voltage levels:
incoherent signals

Adding of two values of the same level give an increase of the total level of (+)3 dB.
This equation is used for electrical adding of incoherent signals,
and for the calculation of the enery level of two loudspeakers.


Adding of two coherent sound pressure levels or voltage levels:
coherent signals
Adding of two values of the same level give an increase of the total level of (+)6 dB.
This is obtained by feeding two side-by-side loudspeakers with the same signal.

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?

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