# What is the correct way to add decibel values?

This is to help clarify my train of thought.

I am aware that in order to add 2 dB (not similar) values . i could follow the post in this link.

The formula is

10*log10((10^(dB1/10))+(10^(dB2/10)))

Here is where I am confused. Let's say i want to add dB SPL values, based on the link above, the formula remains the same to add 2 decibel values.

But since the formula to calculate dB SPL (based on pressure) is 20*log10(p1/p0), where p0 is the ref pressure.

In which case, if I am adding 2 dB SPL values, shouldn't the formula be

20*log10((10^(dB1/20))+(10^(dB2/20))) ?

Why is that not the case ? What am i missing here ?

Depends entirely upon the context in which you are operating. For instance:

• a signal that is peaking at -20dBFS is amplified by 6dB will subsequently peak at -14dBFS.
• a signal that is peaking at -10dBFS is attenuated by 10dB will subsequently peak at -20dBFS.

This works on the basis of simple addition and subtraction.

The 'combination' of more than one point-sources of sound depends entirely on whether the sounds are correlated or non-correlated (incoherent).

For a single point-source of sound radiating at N dBSPL, the addition of additional point sources of sound also radiating at the same level (N dBSPL) will cause the level to increase by 3dB for every doubling of the total number of point-sources. For instance:

• 1 -> N dBSPL
• 2 -> N+3 dBSPL
• 4 -> N+6 dBSPL
• 8 -> N+12 dBSPL
• 16 -> N+15 dBSPL
• etc.

What you are missing from the formulae stated in your post is any information related to the coherence or incoherence of the sound-sources in play.

Coherent sound sources will behave differently to incoherent sound sources.

This is the same reason why you use linear fades when doing crossfades between coherent audio streams and logarithmic fades when fading/editing between incoherent audio streams.

• Therefore if I were to add two dB SPL levels, what would you say the formula is for both the coherent and incoherent sound sources? – whoknowsmerida Nov 6 '19 at 9:47
• that's wonderful explanation, thank you. – whoknowsmerida Nov 7 '19 at 1:43
• The other thing to remember is that when dealing with coherent sources, phase is a very significant factor so I think it is safe to say that any formula that deals with coherent sources is probably only valid when the measurement sensor is equidistant from all sources in the array, otherwise you end up with phase components that cancel each other out rendering the formula moot. – Mark Nov 7 '19 at 2:19