Deutsche Version
● Adding acoustic levels of sound sources ●
Addition of SPL − Sum of levels − voltage , 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 95
Level 2 75
Level 3 65
Level 4
Level 5
Level 6
Level 7
Level 8
Level 9
Level 10
reset
dB
dB
dB
dB
dB
dB
dB
dB
dB
dB
calculate
Total Level 95.047
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)
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The ten octave bands of our hearing range
The formula for the sum level of sound pressures of n incoherent radiating sources is
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
This inserted in the formula for the sound pressure level to calculate the sum level shows
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:
Table for combining decibel levels
0
3.01
Difference between the two levels to be added in dB
1
2
3
4
5
6
7
8
9
2.54 2.12 1.76 1.46 1.19 0.97 0.79 0.64 0.51
Difference between the two levels to be added in dB
10
0.41
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Level difference between the two sound sources
source 1 80
dB
source 2 74
dB
source 3
dB
source 4
dB
reset
total
calculate
dB
Adding of equal loud incoherent sound sources
Level increase Δ L for
n equal loud sound sources
Number of n equal
Level increase
loud sound
Δ L in dB
sources
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
4
↔
Increase of level Δ L
dB
6
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
+30 dB
8
+20 dB
4
+10 dB
2.0 = double
+6 dB
1.52 times
+3 dB
1.23 times
- - - - ±0 dB - - - - - - - - 1.0 - - - - - - −3 dB
0.816 times
−6 dB
0.660 times
−10 dB
0.5 = half
−20 dB
0.25
−30 dB
0.125
−40 dB
0.0625
Log. size
Psycho size
dB change
Ratio
20
15
10
5
4
3
2
-----1----1/2 = 0.5
1/3 = 0.3333
1/4 = 0.25
1/5 = 0.2
1/10 = 0.1
1/15 = 0.0667
1/20 = 0.05
100
31.6
10
3.16 = √10
2.0 = double
1.414 times = √2
- - - - 1.0 - - - - - - 0.707 times
0.5 = half
0.316
0.100
0.0316
0.0100
Field size
Loudness multipl. Amplitude multiplier
Change in Sound
Loudness Level
+43.22 dB
+39.07 dB
+33.22 dB
+23.22 dB
+20 dB
+15.58 dB
+10 dB
- - - - ±0 dB - - -- −10 dB
−15.58 dB
−20 dB
−23.22 dB
−33.22 dB
−39.07 dB
−43.22 dB
Change in Sound
Pressure Level
+26.02 dB
+23.52 dB
+20 dB
+13.98 dB
+12.04 dB
+9.54 dB
+6.02 dB
- - - - ±0 dB - - - -−6.02 dB
−9.54 dB
−12.04 dB
−13.98 dB
−20 dB
−23.52 dB
−26.02 dB
10000
1000
100
10
4.0
2.0 = double
- - - - 1.0 - - - - 0.5 = half
0.25
0.1
0.01
0.001
0.0001
Energy size
Power multiplier
Change in Sound
Power Level
+13.01 dB
+11.76 dB
+10 dB
+6.99 dB
+6.02 dB
+4.77 dB
+3.01 dB
- - - ±0 dB - - -- −3.01 dB
−4.77 dB
−6.02 dB
−6.99 dB
−10 dB
−11.76 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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