Combining sound levels - adding 10 dB levels summing 1/3 octave spl full octave sum summation SPL of non-coherent sound sources identical 10 bands sum noise sound pressure acoustic pressure volts - sengpielaudio
 
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● Adding acoustic levels of sound sources ●
 
Addition of SPL − Sum of levels − voltage , sound, and noise)
 
Summing up to ten non-coherent or uncorrelated  noise sources
 
Non-coherent or incoherent means the signals of the overdubbed channels are irrelative like a violin and a trumpet,
that means having no correlative relationship. Sometimes we say uncorrelated when we mean non-coherent.
 
● Combining decibels - adding up to 10 non-coherent acoustic levels ●
 
The decibel calculator can be used to combine the levels of up to ten non-coherent (incoherent)
electric or acoustic sources when the level of each source is known in decibels (dB).

Level 1   dB
Level 2   dB
Level 3   dB
Level 4   dB
Level 5   dB
Level 6   dB
Level 7   dB
Level 8   dB
Level 9   dB
Level 10   dB
Total Level   dB
Fill in as many sound level boxes as necessary (max 10) and then click the calculate bar, to get the calculated sum. Provided, that each sound source has its own random phasing.

A program to combine as much as thirty (30) noise sources
 
Conversion of sound pressure level to sound pressure and sound intensity

Octave Bands

The ten octave bands of our hearing range
 
The formula for the sum level of sound pressures of n non-coherent radiating sources is
 
SPL Addition 01
 
The reference sound pressure p0 is 20 µPa = 0.00002 Pa = 2 × 10−5 Pa (RMS) ≡ 0 dB.
 
From the formula of the sound pressure level we find
 
SPL Addition 02
 
This inserted in the formula for the sound pressure level to calculate the sum level shows
 
SPL Addition 03
 
LΣ = Total level and L1, L2, ... Ln = sound pressure level of the separate sources in dBSPL.
Non-coherent means: lacking cohesion, connection, or harmony. It is not coherent.
 
For example, adding three levels 94.0 + 96.0 + 98.0:
db addition example

Table for combining decibel levels

Difference between the two levels to be added in dB
0 1 2 3 4 5 6 7 8 9 10
3.01 2.54 2.12 1.76 1.46 1.19 0.97 0.79 0.64 0.51 0.41
Amount to be added to the higher level in order to get the total level in dB

Level adding of two sound sources - sengpielaudio
               Level difference between the two sound sources

source 1  dB
source 2  dB
source 3  dB
source 4  dB
total  dB

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 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.

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.

 
Number of sound sources n:
 		  ↔  Increase of level Δ L:
dB
Formula1   Formula2
 

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

See also:
Adding decibels of one-third octave bands to level of octave band
Combining decibels - adding up to thirty acoustic sound levels
How do Sound Pressure Levels add when listening?

Example: The measurable noise of a motorcycle is at a certain distance 60 dB (A). How big is the total level of 4 motorcycles with the same volume?
Solution: 60 dB (A) + 10 log 4 = 60 + 6 = 66 dB (A).
If you are doing noise measurements of motorcycles you should at least consider the "honesty" of the dBA-readings without low frequencies.

You can easily add up coherent and non-coherent sound level and sound pressure values. It is often desired to add the psychoacoustic perceived loudness or volume. See:

How many decibels (dB) level change is double, half, or four times as loud? How many dB to appear twice as loud (two times)? Here are all the different ratios.
Ratio means "how many times" or "how much" ... Doubling of loudness.

Level
change		 Volume
Loudness		 Voltage
Sound pressure		 Acoustic Power
Sound Intensity
+40 dB 16 100   10000
+30 dB   8    31.6 1000
+20 dB   4 10 100
+10 dB       2.0 = double        3.16 = √10 10
  +6 dB   1.52 times  2.0 = double        4.0
  +3 dB   1.23 times 1.414 times = √2  2.0 = double  
  - - - - ±0 dB - - - - - - - - 1.0 - - - - - - -      - - - - 1.0 - - - - - - -      - - - - 1.0 - - - - -
  −3 dB     0.816 times     0.707 times          0.5 = half
  −6 dB     0.660 times    0.5 = half     0.25
−10 dB    0.5 = half     0.316         0.1  
−20 dB 0.25           0.100         0.01
−30 dB 0.125         0.0316         0.001
−40 dB 0.0625       0.0100           0.0001
Log. size Psycho size Field size Energy size
dB change Loudness multipl. Amplitude multiplier Power multiplier

Ratio Change in Sound
Loudness Level

Change in Sound
Pressure Level

 Change in Sound
Power Level
20 +43.22 dB   +26.02 dB   +13.01 dB  
15 +39.07 dB   +23.52 dB   +11.76 dB  
10 +33.22 dB   +20 dB       +10 dB      
  5 +23.22 dB   +13.98 dB   +6.99 dB
  4 +20 dB       +12.04 dB   +6.02 dB
  3 +15.58 dB    +9.54 dB  +4.77 dB
  2 +10 dB        +6.02 dB  +3.01 dB
  - - - - - 1 - - - - - - - - - ±0 dB - - -- -    - - - - ±0 dB - - - --    - - - ±0 dB - - -- -  
1/2 = 0.5 −10 dB        −6.02 dB  −3.01 dB
     1/3 = 0.3333 −15.58 dB   −9.54 dB  −4.77 dB
  1/4 = 0.25 −20 dB       −12.04 dB    −6.02 dB
1/5 = 0.2 −23.22 dB   −13.98 dB    −6.99 dB
1/10 = 0.1   −33.22 dB   −20 dB        −10 dB     
   1/15 = 0.0667 −39.07 dB   −23.52 dB    −11.76 dB 
1/20 = 0.05  −43.22 dB   −26.02 dB    −13.01 dB 

Noise

Noise is annoying, harassing and unwanted sound. It is not a physical phenomenon, but only mental processes change a sound to noise.
There are a number of definitions of noise. Important ones are:
1 - the acoustic ratio that characterize the noise and by measurable physical sizes, such as the amplitude or the sound pressure level, frequency, and the time behavior of the sound, can be described.
2 - the situational ratio, i.e. location, time and situation in which the person is situate during the occurrence of the noise, and the relation to the activities, intentions and the current being of the person who is exposed to the noise.
3 - the personal ratio of the person who is exposed to the noise, with their acquired cognitive and emotional implications for the sound source. The fact that noise is not
only dependant on physically measurable sizes, but "of more", makes the derivation of methods and calculation methods for the objective description to a problem and explains the problems of noise control, which are often found between the measured noise values and the perceived harassment.
Kurt Tucholsky wrote aptly: "Our own dog does not make noise, it only barks.
 
Castrated sound level values in weighted dBA are added the same way like sound level values in unweighted dB.
 
 
Pro audio equipment often lists an A-weighted noise spec – not because it correlates well with our hearing – but because it can "hide" nasty hum components that make for bad noise specs.
 
Words to bright minds: Always wonder what a manufacturer 
is hiding when they use A-weighting. *)
 

*) http://www.google.com/search?q=Always+wonder+what+a+manufacturer+Rane&filter=0

Formulas for working with sound

1 pascal (Pa)  =  1 newton/m2
                         =  10 dyne/cm2
                         =  10 microbar
                         ≡  94 dB SPL (Sound Pressure Level)
 
Sound Pressure Level (SPL)
Sound pressure level  Lp = 20 × lg (p / p0) in decibels (dB), where
p is the measured pressure as sound field size and
p0 is the reference pressure in the same system of units.
p0  =  20 micropascals  or micronewtons/m2 = 0.00002 Pa
      =  0.0002 microbar or dyne/cm2.
 
This reference pressure
p0 = 0.00002 Pa as a sound field size corresponds to a sound wave in free air with an acoustic intensity (energy) of I0 = 10−12 watt/m2 as a sound energy size.
 
Sound Intensity Level (SIL) or Acoustic Intensity Level
Sound intensity level LI = 10 × lg (I / I0) in decibels (dB), where
I is the measured intensity as sound energy size and
I0 is the reference sound intensity in the same system of units.
I0  =  10−12 watt per m2.
 
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