Adding Decibels

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Let’s say you are preparing to go camping and mountain climbing. When you look through your supplies, you find ropes of many sizes. Two of them are tied in knots. You think that combined the two knotted ropes might be long enough for your plan, but you aren’t sure. So what do you do?

Easy: you untangle the ropes so you can measure them.

Adding decibels works the same way—they need to be untied before you can use them to go adding or subtracting. Sure, a knotted rope might be great for storage or display, but when it comes time for using the rope, you’d better have it untied.

For example, let’s say you have two decibel levels L_1 and L_2 you want to add. Like knotted rope, these levels need to be “un-knotted” before they are useful. To un-knot a decibel level, the formula is quite easy:

Measured\ value = Reference\ value*10^{ \frac{L}{20}}

Note that this formula works for root-power quantities. For power quantities, replace the 10 in this equation with a 20.

If you want to add (or subtract) decibel values, it’s simply a matter to combining the ‘untied’ parts and then wrapping them back up in a decibel knot. Mathematically, that looks like this:

Total\ Level\ (dB) = 20 log_1_0 (\Sigma 10^{\frac{L}{20}})

To subtract levels, make sure you use negative values for L. If you want to add levels based on power quantities, just replace the 20s in the equations with 10s.

With these two equations, you should have all the tools you need to quickly and correctly add or subtract decibel levels. Just remember, decibels are like ropes—you need to untie them before you head off on a big adventure.


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