Signals  Adding Decibels
The logarithmic decibel scale is convenient when adding signal values like sound power, pressure and others from two or more sources.
The decibel (dB) is a logarithmic unit used to express the ratio of two signal values  like power, sound power or pressure, voltage, intensity etc.  where one value is a reference value.
Adding Equal Signal Levels
The total signal level in decibel from equal signal sources can be calculated as
L_{t} = 10 log (n S / S_{ref})
= 10 log (S / S_{ref}) + 10 log (n)
= L_{s} + 10 log (n) (1)
where
L_{t} = total signal level (dB)
S = signal (signal unit)
S_{ref} = signal reference (signal unit)
n = number of sources
L_{s }= signal level from each single source (dB)
The signal units depends on the nature of the signal  W for power, Pa for pressure and so on.
Note!  adding sound pressure levels.
Example  Total Sound Power from Two Identical Fans
For sound power it is common to use 10^{12} W as the reference sound power. Total sound power from two identical fans each generating 1 W in noise power can be calculated as
L_{t} = 10 log (2 (1 W) / (1 10^{12} W))
= 123 dB
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. The "sound" measured with microphones or sensors (meters) are sound pressure.
Adding Equal Signals Units Calculator
Adding Equal Signal Levels (decibels) Calculator
Adding equal signal sources can be expressed graphically
Download and print Adding Signal Level of Equal Sources chart.
Note! Adding two identical sources (doubling the signal) will increase the total signal level with 3 dB (10 log(2)).
Number of Sources  Increase in Sound Power Level (dB) 

2  3 
3  4.8 
4  6 
5  7 
10  10 
15  11.8 
20  13 
Adding Signals from Sources with different Strengths
The total signal level from sources with different strengths can be calculated as
L_{t} = 10 log ((S_{1} + S_{2} ... + S_{n}) / S_{ref}) (2)
Example  Total Sound Power from Two different Fans
The total noise power from two fans  one with sound power 1 W and the other with sound power 0.5 W  can be calculated as
L_{t} = 10 log (((1 W) + (0.5 W)) / (1 10^{12} W))
= 122 dB
Adding two signal sources with different levels can be expressed graphically in decibels as
Download and print Adding Sources with different Signal Levels.
Signal Level Difference between two Sources (dB)  Decibels to Add to the Highest Signal 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 
Example  Adding Sound Power in Decibels
The sound power from one of the fans in the example above can be calculated as
L_{s1 }= 10 log((1 W) / (1 10^{12} W))
= 120 dB
The sound power from the other fan can be calculated as
L_{s2 }= 10 log((0.5 W) / (1 10^{12} W))
= 117 dB
The difference in decibel is
L_{s1}  L_{s2 }
= (120 dB)  (117 dB)
= 3 dB
From the table or diagram above a difference of 3 dB requires that 2 dB must be added to the highest sound pressure source as
L_{t }= (120 dB) + (2 dB)_{ }
= 122 dB
Related Topics

Acoustics
Room acoustics and acoustic properties, decibel A, B and C, Noise Rating (NR) curves, sound transmission, sound pressure, sound intensity and sound attenuation. 
Measurements and Instrumentation
Measurement and instrumentation strategies. 
Noise and Attenuation
Noise is usually defined as unwanted sound  noise, noise generation, silencers and attenuation in HVAC systems.
Related Documents

Decibel
Logarithmic unit used to describe ratios of signal levels  like power or intensity  to a reference level. 
Decibel A, B and C
Sound pressure filters that compensates for the hearing sensed by the human ear. 
Logarithms
The rules of logarithms  log_{10} and log_{e} for numbers ranging 1 to 1000. 
Noise Attenuation in Rotary Heat Exchanges
Sound attenuation vs. frequency in rotating heat exchangers. 
Noise generated in Air Ducts
Estimate noise generated by air flow in ducts. 
Noise generated in Blade Dampers
Sound power noise generated by blade dampers in ventilation systems. 
Propagation of Outdoor Sound  Partial Barriers
The transmission of outdoor sound through and around barriers  the Fresnel Number. 
Sound Intensity, Power and Pressure Levels
Introduction to decibel, sound power, intensity and pressure. 
Sound Power
Sound power from sources like fans, jet engines, cars, humans and more. 
Sound Pressure
Sound Pressure is the force of sound on a surface perpendicular to the propagation of sound.