Decibels are logarithmic "units", they may not be added linearly like other figures.

In most cases we will add uncorrelated signals as noise or music. If a sound source creates a sound level (SPL) of L 1 = 60 dB and another source with L 2 = 60 dB is added, then it is not the level of 120 dB, but gives an incoherent (noncoherent) summing of the signal level of 63 dB. If both values are equal, it is easy.

More than 3 dB greater than the higher of the two incoherent levels is not possible for the total sum in decibels.

See also the other case:

● Total level adding of electrical coherent signals.

Sum calculation of two incoherent signals - "Acoustic level addition"

1st sound source

Level L 1 dB |

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+ 2nd sound source

Level L 2 dB |

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| Total level from

both sources

= dB Incoherent signals! "Power sum"

Adding amplitudes (and levels)

Power sum

incoherent (90°)

√ (1² + 1²) = 1,414... Voltage sum

coherent (0°)

1 + 1 = 2

Adding of two incoherent (noncoherent) sound pressure levels or voltage levels:





Adding of two values of the same level results 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 energy level of two loudspeakers.



Adding of two coherent sound pressure levels or voltage levels:



Adding of two values of the same level results an increase of the total level of (+)6 dB.

This is obtained by feeding two side-by-side loudspeakers with the same signal.



Level difference between the two sound sources

Adding of two different acoustical levels

For the sound level of n incoherent radiating sound sources we get:





p 0 is the reference value of the sound pressure. Auditory threshold at 1 kHz = 0.00002 Pa = 20 µPa.



Level adding of up to four sound sources

Source 1 dB Source 2 dB Source 3 dB Source 4 dB Total sum dB

Adding of equal loud incoherent sound sources

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(Δ 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 × log 10 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 × log 10 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 × log 10 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 × log 10 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 strong incoherent (non-coherent) sound sources Number of sound sources n

↔ Increase of level Δ L

dB

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





What does sound level mean?