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Sound Level Maths

Decibel mathematics may seem strange as numbers don't behave in the ways you expect. That's because the numbers are based on logarithms.

 

This can be confusing as it leads to a lot of strange maths - for instance, 1 + 1 = 4! It also has an interesting property of changing multiplication into addition. For example, when you multiply by 2, you add 3 dB, when you multiply by 4, you add 6 dB. 

 

This also means that each increase of 10 dB represents a tenfold increase. E.g. 70 dB has 10 times more sound energy than 60 dB, and 100 times more sound energy than 50 dB.

There are a couple of other quirks: zero dB isn't actually zero and negative dBs represent positive (but very small) values. This is because dB represents a ratio compered to a reference value and itself is not an actual value. 

Below are some simple calculators showing how it works.

Addition

dBAddition Eqn2.png

dB

+

dB

=

dB

Subtraction

dBDivision Eqn2.png

dB

-

dB

=

dB

Multiplication

dBMultiply Eqn_edited.png

dB

x

=

dB

Division

dBDivision Eqn.png

dB

/

=

dB

These equations are only true when the sounds are uncorrelated

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