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| 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
The ten octave bands of our hearing range
The formula for the sum of the sound pressure levels 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.
Table for combining decibel levels
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 3.0 | 2.5 | 2.1 | 1.8 | 1.5 | 1.2 | 1.0 | 0.8 | 0.6 | 0.5 | 0.4 |
Adding equal loud sound sources
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Formulas: Δ L = 10 × log n or n = 10Δ L / 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 = 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. |
Calculator: Adding level of equal loud sound sources
| To use the calculator, simply enter a value. Then use the TAB key or click the mouse in an empty area of the page to update the result. Calculator works in both directions of the ↔ sign. |
The total level in dB is the level of one sound source plus the increase of level in dB.
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See also: |
| 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 incoherentsound 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 (twofold)? Here are all the different factors. Factor 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 fold | 2.0 = double | 4.0 |
| +3 dB | 1.23 fold | 1.414 fold = √2 | 2.0 = double |
| - - - - ±0 dB - - - - | - - - - 1.0 - - - - - - - | - - - - 1.0 - - - - - - - | - - - - 1.0 - - - - - |
| −3 dB | 0.816 fold | 0.707 fold | 0.5 = half |
| −6 dB | 0.660 fold | 0.5 = half | 0.25 |
| −10 dB | 0.5 = half | 0.316 | 0.01 |
| −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. quantity | Psycho quantity | Field quantity | Energy quantity |
| dB change | Loudness multipl. | Amplitude multiplier | Power multiplier |
| Factor | Change in Sound Loudness Level |
Change in Sound |
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. Noise 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 factors that characterize the noise and by measurable physical quantities, such as the amplitude or the sound pressure level, frequency, and the time behavior of the sound, can be described. 2 - the situational factors, ie location, time and situation in which the person is situated 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 factors 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 quantities, 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. |
Formulas For Working With Sound
| 1 Pascal (Pa) = 1 Newton/m2 = 10 dyne/cm2 = 10 microbar = 94 dB SPL Sound Pressure Level (SPL) Sound Pressure Level Lp = 20 × lg (p / p0) in decibels (dB), where p is the measured pressure and p0 is a 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 quantity corresponds to a sound wave in free air with an acoustic intensity (energy) of I0 = 10−12 Watt/m2 as a sound energy quantity. Sound Intensity Level (SIL) or Acoustic Intensity Level Sound Intensity Level LI = 10 × lg (I / I0) in decibels (dB), where p is the measured pressure and p0 is a reference pressure in the same system of units: I0 = 10−12 Watt / m2. |
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