# Decibel: A practical understanding



## DebayanB (Apr 30, 2022)

Hello community,

I have been involved in music production and composition for almost 2 years now and have a very basic understanding of the essential terms one comes across in this field, in general. However, one term that still eludes my understanding is the very unit of sound level: Decibel (dB). I have two questions:

1. From a DAW point of view, we are all accustomed to seeing a meter starting all the way for -60dB and going all the way up to 6dB mostly). I have tried and failed to understand why it is in negative as it makes no practical sense to me. A clear, (not necessarily) concise explanation would be very helpful.

2. In life, I hear the term decibel refer to all sorts of things. For instance, I found that CPU fans have an approximate <21dB sound output. What does this mean? In comparison to DAWs, this would be deafening and yet I am aware that helicopters emit over 150dB. And another source mentioned noise in dbA unit. 

I am thoroughly confused and lack any sort of *practical understanding* of these terms. Any help is hugely appreciated.

Regards,
Debayan


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## d.healey (Apr 30, 2022)

Decibel is a unit that is relative to a particular scale. So for example dB FS is full scale, dB SPL is sound pressure level, dBv is relative to voltage.

So the unit can be reused in different contexts and have different meanings.

Wikipedia has a good list of different scales that use the dB unit - https://en.wikipedia.org/wiki/Decibel#Suffixes_and_reference_values


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## Pier (Apr 30, 2022)

Like David said, a decibel is only a unit of relative value.

The basic idea is "bottle A contains double the water compared to bottle B". So you have a base reference (bottle B) and the actual value (bottle A).

The other thing to understand is that decibels are logarithmic and not linear. So doubling is increasing by 3dbs, quadrupling 6dbs, etc.

Why use decibels instead of a linear value like kgs, pounds, etc? Well, the thing with sound is that it would be a mess to use a linear value since it can go from tiny values to extreme huge values. Imagine you had to say "oh increase the gain by 10000000 units" vs "increase the gain 70dbs".

The final piece of the puzzle is that you need a reference value. Which is why there are many types of decibels. Eg: dB SPL (sound pressure level) are relative to 20 micropascals (a measure of pressure). So 6db SPL would be 80 micropascals which is really completely inaudible.

So now we can make up a new unit called dB BB (bottle B) and say "bottle A has 3dB(BB)" or something.


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## d.healey (Apr 30, 2022)

Pier said:


> Why use decibels instead of a linear value like kgs, pounds, etc?


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## shawnsingh (May 2, 2022)

DebayanB said:


> 1. From a DAW point of view, we are all accustomed to seeing a meter starting all the way for -60dB and going all the way up to 6dB mostly). I have tried and failed to understand why it is in negative as it makes no practical sense to me. A clear, (not necessarily) concise explanation would be very helpful.





DebayanB said:


> 2. In life, I hear the term decibel refer to all sorts of things. For instance, I found that CPU fans have an approximate <21dB sound output. What does this mean? In comparison to DAWs, this would be deafening and yet I am aware that helicopters emit over 150dB. And another source mentioned noise in dbA unit.



Here's a mental journey that might help. Not how decibels were conceived as I understand, but good for learning:

Step 1: Any measurement, absolute or relative, can technically be re-interpreted as a ratio compared to some reference value. Example: 100 degrees Celsius? That's a ratio where you have 100 times more than one unit of degrees Celsius. 

Why bother with this? it becomes clearer when we say the same thing in a different way: _any quantitative measurement, absolute or relative, implicitly has some underlying "reference" measurement, which is the "unit" of measurement_. So the idea of using ratios helps make the "unit of measurement" explicit. This is especially useful when the "unit" of measurement is flexible and abstract, like it is when measuring the strength of a signal versus noise on an analog wire (where the "unit" is awkwardly relative to the strength of the signal), or when representing digital audio (which could have any "loudness" depending on your volume knob on the playback system).

Step 2: Many things about human perception, hearing changes in air pressure being one of them, are often perceived on a logarithmic scale - small variations at small levels may have the same perceived impact as larger variations at large levels. Small variations at large levels are usually not as perceivable. Sure enough, ears are sensitive to changes in air pressure of even less than 20 micro Pascals (0 dB SPL) all the way to 20,000,000 micro Pascals (120 dB SPL). If we were to be very picky, as far as I understand, human hearing does not precisely follow a pure logarithmic scale. There are other scales like Bark and Mel that are not quite logarithmic but derived from ideas in psychoacoustics and human perception, but still they turn out to be roughly logarithmic.

Step 3: Combining these two things, you can get the unit of Bel:
log10 (power / reference_power_level).
And in digital audio, we often work with amplitudes instead of powers, which are related to each other by a square factor. Remembering the math of logarithms, that square factor becomes a multiplicative factor in the logarithmic domain -->
2 * log10 (amplitude / reference_amplitude)

And, historically it was convenient to usually talk about this measurement in tenths, so they decided to make decibel the common used measurement:
20 * log10 (amplitude / reference_amplitude)

This last version is the most useful when thinking of sound pressure levels or digitally represented audio amplitudes. I think the electrical engineers have more reasons to think of power measurements instead of amplitudes.

Step 4: follow the math.
- if amplitude is less than reference, you get negative numbers
- if amplitude is greater than reference you get positive numbers
- if amplitude == reference you get 0
- every time you double power, you increase by 3 dB
- every time you double amplitude, you increase by 6 dB

Step 5: consider some typical decibel scales
- dBV, dBu --> (the capitalization of that letter matters) use volts as a reference
- dB SPL --> uses 20 micro Pascals sound pressure as the reference. Most things are louder than this, so the range that people usually think about is something like 0 to +140 dB SPL. Interestingly, good human hearing in 2-4 kHz area can hear quieter than this, which would be negative dB SPL numbers - so something like -5 dB SPL is awkward but legitimate!
- dBFS --> reference is the RMS of a sine wave that has a peak amplitude of "max representable integer" or "1.0". This is the AES standard definition, but I think it sometimes gets ignored.
- dBFS slightly incorrect but common --> define reference directly as "max representable integer" or "1.0", ignoring the RMS part of a sine wave. On this scale, the RMS of a sine wave is -3 dB, and sure enough, everything using this version of dBFS would measure 3 dB less than the standard definition of dBFS that uses the RMS of the full scale sine wave.
- for standard integer representations of audio, it's not possible to exceed +3 dBFS. (or 0 dBFS using the slightly incorrect convention). But for floating-point representations of audio, the full-scale reference is 1.0. So it's easy to represent audio signals arbitrarily louder than 0 dBFS.

Step 6: it's common to include "frequency weighting" as a part of some decibel scales.
- dBA, dBC - different frequencies are emphasized or de-emphasized before a measurement is taken.

And one pitfall to be aware of - many of these decibel scales are only meaningful with RMS measurements, not instantaneous amplitudes. For example, dB SPL. And also frequency weighting is not meaningful for an instantaneous amplitude measurement. When in doubt, be careful interpreting any dB value as an instantaeous measurement.

And finally this brings up the question "why is full scale used as the reference for decibels in digital audio? isn't it awkward since that makes it negative numbers? Why couldn't it be something more like dB SPL?" So, if you wanted the scale to be positive instead, you can ask yourself, what reference value would you use? An amplitude of 0 would cause divide-by-zero math mayhem. So then you'd be forcing yourself to use RMS measurements and defining a very small value to be reference. But then, what is the purpose of doing that - it won't necessarily match dB SPL anyway because someone can always turn their volume knob and change everything by +/- 50 dB. Also, what about converting between different digital representations - 16-bit versus 24-bit versus floating-point? If you have audio in 16-bit and convert it to 24-bit, you take advantage of that added resolution by making all amplitudes proportionally larger - but do we want to interpret that as making the audio signal louder? Probably not? Using full scale reference for digital audio avoids a lot of these problems. So while I have no idea what insight people had when it became the convention, these are some of the compelling reasons why it's nice that digital audio is represented this way, with reference as the "max".


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