Combining sound levels adding 10 dB levels summing 1/3 octave spl full octave audio logarithmic decibel scale sum summation SPL of incoherent 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 SPLSum of levelsvoltage , sound, and noise
 
Summing up to ten incoherent or uncorrelated  noise sources
 
Incoherent or noncoherent 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 incoherent.
Given two incoherent sources their combined effect is the sum of their acoustic power.
 
Combining decibels - adding up to 10 incoherent acoustic levels ●
 
The decibel calculator can be used to combine the levels of up to ten incoherent (noncoherent)
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

Adding Amplitudes and Levels (coherent and incoherent)

Octave Bands

The ten octave bands of our hearing range
 
The formula for the sum level of sound pressures of n incoherent 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.
Incoherent means: lacking cohesion, connection, or harmony. It is not coherent.
 

For example, adding of threedecibel values, that means levels 94.0 + 96.0 + 98.0:
dB addition of 3 values

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
Difference between the two levels to be added 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 incoherent 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 incoherent 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 incoherent 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 incoherent 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 incoherent 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

To use the calculator, simply enter a value.
The calculator works in both directions of the
sign.

 Equal loud incoherent sound sources
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 Amplitudes and Levels
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?
Total level adding of incoherent acoustical sound sources
Total level adding of coherent signals
The human perception of loudness
Subjectively perceived loudness, objectively measured sound pressure, and theoretically calculated sound intensity

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 incoherent 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 sound pressureas a sound field size corresponds to a sound wave in free air with an acoustic pressure of
p0 = 0.00002 Pa (N/m²).
 
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.
 
This reference sound intensity as a sound energy size corresponds to a sound wave in free air with an acoustic intensity (energy) of I0 = 10−12 watt/m2.

What does sound level mean?

A reduction of the sound power level of the sound source by 6 dB is resulting in a reduction of the sound pressure level and the sound intensity level at the location of the receiver by also 6 dB, even if the sound power drops to a factor of 0.25, the sound pressure drops to a factor of 0.5 and the sound intensity drops to a factor of 0.25. The reference value for the sound level was chosen so that with a characteristic acoustic impedance of Z0 = ρ · c = 400 N·s/m3 the sound intensity level results in the same value as the sound pressure level. We therefore simply speak of the "sound level" and leave it open whether sound pressure level or sound intensity level is meant.
 
 
Sound engineers and sound protectors ("ear people") think by the short word
"
sound level" simply of "sound pressure level" (SPL) as sound field quantity.
 
Acousticians and sound protectors ("noise fighters") mean by the short word
"
sound level" probably "sound intensity level" as sound energy quantity.
Equating sound pressure with sound intensity must cause problems.   I ~ p2.
 
 
 
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