### Decibels Demistified

What are decibels and why do we use them?

Most people have heard of decibels, and anyone working in audio or acoustics probably uses them on a daily basis – but they are still widely misunderstood and shrouded in mystery. Within this short blog post, we are going to try to understand them and remove the confusion surrounding them.

OK, so the human ear is an incredible instrument, capable of hearing a very wide range of noises at varying volume levels – from a pin drop to a jet engine. The ear essentially works by sensing cyclic variations in atmospheric pressure, which is what we generally refer to as sound. These pressure fluctuations are measured in pascals (Pa).

The quietest sound which we can perceive is around 20 micropascals (that’s 0.00002 pascals), and at the other end of the scale we can hear sounds up to 200 Pascals, although it would be a very unpleasant and painful experience. Looking at those values, 0.00002 to 200, you can see that there is a huge range of pressure levels which can be detected by the ear and it would be very impractical for acousticians and audio professionals to use this scale to define noise levels.

What we really want to do is drastically compress this range of potential noise values to make it more manageable – and the solution is the decibel. This is how it works. Because we know the threshold of human hearing (give or take) is 20 micropascals, we take this as a reference value. We then take the pascal value of the sound we are interested in, let’s say 1 pascal for example, and calculate the ratio between the two numbers.

But first, as we are dealing with sound pressure we need to square the two numbers in order to make the ratio relate to acoustic intensity (as intensity is proportional to pressure squared).

So, 1 squared / 0.00002 squared = 2500000000. Still not a very practical number! We take this and use a logarithmic function to compress the range of values. If you can’t quite remember back to maths class, a log function tells you the power you need to raise a base value to (usually 10) to get the number you are interested in, so for example: log of 1000 = 3 (because 10^3 = 10 x 10 x 10 = 1000).

In our example, log of (1 pascal squared / 20 micropascals squared) = log of 1 / 0.0000000004 = log (2500000000) = 9.39.

At this point, we have a value in Bels, named after Alexander Graham Bell, inventor of the telephone among other things (this is why decibel (dB) has the capital B and small d). The issue we have now with our value of 9.39 is that it a bit low, and a scale of 0 to around 10 doesn’t give us much resolution (I know what you’re thinking, that was the whole point wasn’t it?!). But luckily there is a very simple solution, we multiply the log ratio by ten – which is where the name comes from (Deci-Bel i.e. 10 times the Bel). So in our example, 9.39 become: 9.39 x 10 = 93.9dB.

And that is it basically, obviously there are many other uses for the decibel, which we’ll discuss another time, but the only significant difference is the reference values (rather than 20 micropascals). It might seem a bit complicated at first, but effectively all you need to know is that a decibel is simply the log of the ratio of a pressure level versus a reference value (the threshold of hearing in this case).

Incidentally, the value of 1 pascal is what is produced by your handheld calibrator – which is why 94.0dB is used as a calibration level – one for the acoustician pub quiz.

Hopefully that has helped to clear up some of the confusion – but if not, please feel free to get on touch – we are always happy to hear from you.

NCSL Team