What is a Decibel?

What is a Decibel (dB)??? Well, one answer is it is one tenth of a Bel (B), but that is not helpful in the least is it. Does this make more sense, in one of the contexts that the Decibel is used, it is a measuring unit of sound pressure, or put another way, how much the air pressure in a sound wave varies from the pressure of the still air in the same environment, or it may be the ratio between two or more sources of sound wave pressure.

Now… we have to stop here for a while, and again go back to our maths class at high school. Remember logarithms? I can vaguely. Logarithms are those horrible calculations where you use powers of numbers, that is multiplying a number by itself a given number of times. Ah yes, through the distant fog I remember, ten to the power of one (101) is ten one time only (= 10), ten to the power of two (102)is ten multiplied by itself twice (10 *10 =100) ten to the power of three (103) is ten multiplied by itself three times (10*10*10 = 1000) and so on.

OK so what, well the Decibel measuring scale is logarithmic and that’s important to get a handle on. Let’s first consider the base measuring unit the Decibel is derived from, the Bel, named after Alexander Graham Bell. A sound pressure that measures one Bel (10 Decibels for the geniuses amongst us) has a certain value, call it anything you like, why not pressure X, everyone else uses X. What would a sound pressure of two Bels equal? Noooooo…. not X*2, it would equal X2 or X to the power of two. If X equalled ten then X2 would equal 100. Two Bels is TEN times stronger than one Bel. We can take that a bit further….. what about 3 Bels? Again assuming X equals 10, 3 Bels would be X3! That’s a HUNDRED times stronger. We do not usually use the Bel (B) as a measuring standard, its numbers are too big for most practical purposes, we use one tenth of a Bel, the Decibel (dB) as the measuring standard.

Let’s leave the maths mostly alone for a while, to everyone’s releif, and ask a basic question. Why use a logarithmic scale to measure sound pressure anyway? Why not use a simple linear scale where you don’t use powers, just ordinary old multipication? The answer is our ears have an incredibly large dynamic range, that is the range from the very softest sound we can hear, to the very loudest sound we can discriminate before our hearing mechanisms are saturated and can no longer discriminate any differences in loudness. If we used a simple linear graph to plot this dynamic range you’d end up with something about as long as ten rolls of toilet paper! A logarithnic scale on the other hand, because its numbers increase so rapidly lets you “squash” that information into something that is reasonable to manage.

We do the same thing with measuring earhquakes by the way, because the amount of energy released in an eathquake can cover an enormous range of values, we use the Richter scale, which you guessed it, is a logarithmic scale. An eathquale of magnitide 2 is TEN times stronger than magnitude 1 etc.

Right students, we are now ready for the nitty gritty.
First, what is the baseline or reference sound pressure we use to measure all other sound pressures against, that is what sound pressure has a value of 0 dB? The intuitive response to that question would be to say “absolute silence”. However that can’t really be tightly defined, so those that know these things have set the reference level as the softest sound a young person with undamaged hearing can hear. You won’t believe how little sound pressure that is .. 20 micropascals!! That is two ten billionths of atmospheric pressure. Incredible isn’t it, our ears are such beautiful acoustic devices that they can detect a difference in pressure that small.

There is a practical “rule of thumb” we can use to describe sound pressure levels that uses everyday metaphors:-
0dB …. The very softest sound a young person with good hearing can discrininate.’
30dB …. A quiet night, with just some distant sounds of chirping crickets, or slight rustling of leaves in a breeze. A very soft whisper.
60dB …. Around the average sound pressure of a person speaking normally.
90dB …. A jack hammer.
110dB …. A rock concert.
120dB …. A jumbo jet on full throtle taking off.
150dB ….. A high powered rifle shot.
250dB ….. A large bomb explosion.

We are all aware that exposure to very loud noises can damage our ears. Damage can occur instantly when sound pressure approaches 175bB or more. Sound wave pressures of those intensities will literally blow our eardrums in. More subtle, but just as nasty is prolonged exposure to sound pressures around 90dB – 110dB. This can cause slow cumulative ear damage, often leading to a loss of the ability to hear high frequencies over a period of time. If your ears are ringing after being exposed to sound the general rule is that is damaging.

This is not the end of the story with the decibel. When Mr Lee DeForest invented the vacuum tube (valve) at the beginning of the 20th century it was possible to amplify very small electical signals. So, a measuring scale of amplification was needed for the first time. Amplification works logarithmically. No problem, a very convenient logarithmic measuring scale already existed the decibel! This measuring scale was adapted for electronics. We talk about amplification in dB (actually dBu dBv but don’t get too worried about that). Anyone who has seen a professional amplifier or mixer will notice that the knobs are marked in dB, not 1,2,3,4 etc. The reason is that those who know the formulas and can work a calculator can work out very precise measurements from those knob settings. One last comment, in electronics, unlike sound, you can have deamplification as well as amplification so in electronics you will see -dB (negative decibels) meaning a signal coming out is weaker than a signal going in.