Adding Decibels

The logarithmic decibel scale is convenient calculating sound power levels and sound pressure levels for two or more sound source.

Adding Equal Sound or Noise Power Sources

The resulting sound power when adding equal sound power sources can be expressed as: 

L_wt =  10 log(n N / N₀)

    = 10 log(N / N₀) + 10 log(n) 

    = L_ws + 10 log(n)         (1)
where
L_wt = the total sound power level (dB) 
L_ws= sound power level from each single source (dB)
N = sound power (W)

N₀ = 10^-12 - reference sound power (W)
n = number of sources

Adding Equal Sound Power Calculator

N - sound power (W)
N₀ - reference sound power (W)

n - number of sources
Sound Power Level (dB) :

L_ws - sound power level (dB)

n - number of sources
Sound Power Level (dB) :

Adding of equal sound power sources can be expressed graphically

Note! Adding of two identical sources will increase the total sound power level with 3 dB (10 log(2)).
Sound power and sound power level are often used to specify the noise or sound emitted from technical equipment like fans, pumps or other machines.
Sound measured with microphones or sensors are sound pressure.

Adding Equal Sound Pressure Levels

The resulting sound pressure level when adding equal sound pressure can be expressed as: 

L_pt = L_ps + 10 log(n)      (2)
where 
L_pt = total sound pressure level (dB)
L_ps = sound pressure level from each single source (dB)
n = number of sources

Adding Equal Sound Pressure Levels Calculator

L_ws - sound power level (dB)

n - number of sources
Sound Pressure Level (dB) :

Number of Sources	Increase in Sound Power Level (dB)	Increase in Sound Pressure Level (dB)
2	3	6
3	4.8	9.6
4	6	12
5	7	14
10	10	20
15	11.8	23.6
20	13	26

Adding Sound Power from Sources with different Sound Powers 

The sound power level from more than one source can be calculated as

L_wt =  10 log( (N₁ + N₂ ... + N_n) / N_o)    (3)

Adding two sources at different levels can be expressed graphically as

Sound Power Level Difference between two Sound Sources (dB)	Added Decibel to the Highest Sound Power Level (dB)
0	3
1	2.5
2	2
3	2
4	1.5
5	1
6	1
7	1
8	0.5
9	0.5
10	0.5
> 10	0