All you need to know about the decibel

Here is an bird's eye view on the decibel and how understanding it can be useful if you work as a sound designer, sound mixer or even just anywhere in the media industry.

I've included numbered notes that you can open to get more information. So, enter, the decibel:

The Decibel is an odd unit. There are three main reasons for this: 

1: A Logarithmic Unit

Firstly, a decibel is a logarithmic unit1. Our brains don't usually enjoy the concept of logarithmic units since we are used to things like prices, distances or weights, which usually grow linearly in our every day lives. Nevertheless, logarithmic units are very useful when we want to represent a vast array of different of values.

Let's see an example: If we take a value of 10 and we make it 2, 3 or 5 times bigger, we'll see that the resulting value will get huge pretty fast on a logarithmic scale.2
  1. Note that I will use logarithmic units and logarithmic scales interchangeably.

  2. I'm using a logarithm to base 10. Is the easiest to understand since we use the decimal system.

 
How much bigger? Value on a linear scale Value on a logarithmic scale
1 Time 10 10
2 Times 20 100
3 Times 30 1000
4 Times 40 10000
5 Times 50 100000
 
The reason behind this difference is that, while the linear scale is based on multiplication, the logarithmic scale uses exponentiation.3 Here is the same table but with the math behind it, including the generic formula:
  1. And actually, the logarithm is just the inverse operation to exponentiation, that's why sometimes you will see exponential scales or units. They are basically the same as a logarithmic ones.

 
How much bigger? Value on a linear scale Value on a logarithmic scale
1 Time 10 (10*1) 10 (101)
2 Times 20 (10*2) 100 (102)
3 Times 30 (10*3) 1000 (103)
4 Times 40 (10*4) 10000 (104)
5 Times 50 (10*5) 100000 (105)
X Times 10*X 10X
 

As you can see, with just a 5 times increment we get to a value of a hundred thousand. That can be very convenient when we want to visualise and work with values on a set of data ranging from dozens to millions. 

Some units work fine on a linear scale because we usually move within a small range of values. For example, let's imagine we want to measure distances between cities. As you can see, most values are between 3000 and 18000 km, so they fit nicely on an old fashioned linear scale. It's easy to see how the distances compare.

Now, let's imagine we are still measuring distances between cities, but we are an advanced civilization that has founded some cities throughout the galaxy. Let's have a look:

As you can see, the result is not very easy to read. Orion is so far away that all other distances are squashed on the chart. Of course, we could use light years instead of km and that would be much better for the cities on other stars but then we will have super low, hard to use numbers for the earth cities. Another solution would be measure earth cities in kllometres and galaxy cities in light years but then we wouldn't be able to easily compare the values between them. 

The logarithmic scale offers us a solution for this problem since it easily covers several orders of magnitude. Here is the same distance chart, but on a logarithmic scale, I just took the distances in kilometres and calculated their logarithms.

This is much more comfortable to use, we can get a better idea of the relationships between all these distances.

Like the city examples above, some natural phenomena that span through several orders of magnitude, are more comfortably measured with a logarithmic scale. Some examples are pH, earthquakes and... you guessed it, sound loudness. This is the case, because our ears are ready to process both very quiet and very loud sounds.4
  1. It seems like we animals experience much of the world in a logarithmic way. This also includes sound frequency and light brightness. Here is a cool paper about it.

So the take away here is that we use a logarithmic scale for convenience and because it gives us a more accurate model of nature.

2: A Comparative Unit

Great, so we have now an easy to use scale to measure anything from a whisper to a jet engine, we just need to stick our sound level meter out of the window and check the number. Well, is not that simple. When we say something is 65dB, we are not just making a direct measurement, we are always comparing two values. This is the second reason why decibels are odd, let me elaborate:

Decibels are really the ratio between a certain measured value and a reference value. In other words, they are a comparative unit. Just saying 20dB is incomplete in the same way that just saying 20% is incomplete. We need to specify the reference value we are using. 20% percent of what? 20dB respect to what? So, what kind of reference value could we use? This brings me to the third reason:

3: A Versatile Unit

Although most people associate decibels with sound, but they can be used to measure ratios of values of any physical property. These properties can be related to audio (like air pressure or voltage) or they may have little or nothing to do with audio (like light or reflectivity on a radar). Decibels are used in all sort of industries, not only audio. Some examples are electronics, video or optics.

OK, with those three properties in mind, let's sum up what a decibel is.

A decibel is the logarithmically expressed ratio between two physical values

Let that sink in and make sure you really get those three core concepts.
Now, let's see how we can use them to measure sound loudness, that's why we were here if I remember correctly.

In space, nobody can hear you scream

14784812262_6f1534b0e2_b.jpg

As much as Star Wars is trying to convince us on the contrary, sound's energy needs a physical medium to travel through. When sound waves disturb such mediums, there is measurable pressure change as the atoms move back and forth. The louder the sound, the more intense this disturbance is.

Since air is the medium through which we usually experience sound, this gives us the most direct and obvious way of measuring loudness: we just need to register how pressure changes on a particular volume of air. Pressure is measured in Pascals, so we are good to go. But wait, if this is the most direct way of measuring loudness couldn't we just say that a pair of speakers are capable of disturbing the air with a pressure of 6.32 Pascals and forget about decibels?

Well, we could, but again, it wouldn't be very convenient. While the mentioned speakers can reach 6.32 Pascals and this seems like a comfortable number to manage, here are some other examples, from quiet to loud:

 
Source Sound Pressure in Pascals (Pa) Sound Pressure (mPa)
Microsoft's Anechoic Chamber 0.0000019 0.0019
Human Threshold of Hearing @ 1 KHz 0.00002 0.02
Quiet Room 0.0002 0.2
Normal Conversation 0.02 20
Speakers @ 1 meter 6.32 6320
Human Threshold of Pain 63.2 63200
Jet Engine @ 1 meter 650 650000
Rifle shot @ 1 meter 7265 7265000
 

Unless you love counting zeros, that doesn't look very convenient, does it? Note how using Pascals is not very confortable with quiet sounds while mPa (a thousandth of a Pascal) doesn't work very well with loud ones. If our goal is to create a system that measures sound loudness, one of the key things we need is that the unit we use can comfortably cover a large range of values. Several orders of magnitude, actually. To me, that sounds like a job for an logarithmic unit.

Moreover, maybe measuring just naked Pascals doesn't seem like a very useful thing to do when our goal is to just get an idea of how loud stuff is. A better way of doing this, could be to compare our measured value to a reference value and get the ratio between the two. This is starting to sound an awful lot like our previous definition of a decibel! We are getting somewhere.

So, what could we use as a reference level to measure the loudness of sound waves on the air? If you have a look at the table above, you'll notice a very good candidate: the human threshold of hearing. If we do this, 0dB would be the very minimal pressure our ears can detect and after that, the numbers would go up in a comfortable scale as we go up in intensity. Even better, if we measure sounds that are below our ear's threshold the resulting number will be negative, indicating not only that the sound would be imperceptible for us but also saying by how much. That's an elegant system right there. I'm starting to dig decibels.

Now, let's look at the previous Pascals table, but adding now the corresponding decibel values:

 
Source Sound Pressure in Pascals dBSPL
Microsoft's Anechoic Chamber 0.0000019 -20.53
Human Threshold of Hearing @ 1 KHz 0.00002 0
Quiet Room 0.0002 20
Normal Conversation 0.02 60
Speakers @ 1 meter 6.32 110
Human Threshold of Pain 63.2 130
Jet Engine @ 1 meter 650 150
Rifle shot @ 1 meter 7265 171
 

That looks like a much easier scale to use. Remember that dBs are used to measure both very quiet things like anechoic chambers and very loud stuff like space rockets. This scale does a better job for the whole range of human audition, it is fine tuned to those microphones we carry around and call ears.

Decibel Flavours

Did you notice that on the table above there is a cute subindex after dB that reads SPL? What's up with that? That subindex stands for Sound Pressure Level and is a particular flavour of decibel. Since decibels can be based on any physical property and since they can use any reference value, we can have many different flavours of decibels depending of which measured property and reference value is more convenient to use in each case.

In the case of dBSPL, this type of decibel is telling us two things. Firstly, that the physical property we are using is pressure. Secondly, that our reference value is the threshold of human hearing. This is fine for measuring loudness on sound waves travelling through the air but, is audio information capable of travelling through other mediums?
AcousticSession.jpg

We have learned to transform the frequency and amplitude information contained in sound waves in the air into grooves in a record or streams of electrons in a cable. That's a pretty remarkable feat that deserves its own post but for now let's just consider that we are able to "code" audio information into flows of electrons that we can measure.

Since dBs can used with any physical property, we can use units from the realm of electronics like watts or volts to measure loudness in a electrical audio signal. In this sense, both pascals and volts give us an idea of how intense a sound signal is, even though they refer to very different physical properties.

So, we need to establish which units and reference values will be useful to use to build new decibel flavours. We also need to label our particular flavour of dB somehow. This is usually done using a subindex (dBSPL) or a suffix (dBu).

Let's have a look at some of the most used decibel flavours:

dB Unit Property Measured (Unit) Reference Value Used on
dBSPL Pressure (Pascals) 2*10-5 Pascals
(Human Threshold of Hearing)
Acoustics.
dBA, dBB, and dBC Pressure (Pascals) 2*10-5 Pascals
(Human Threshold of Hearing)
Acoustics when accounting for
human sensitivity
to different frequencies.
dBV Electric potential (Volts) 1 Volt Consumer audio equipment.
dBu Electric potential (Volts) 0.7746 Volts Professional audio equipment.
dBm Electric Power (Watts) 1mW Radio, microwave and
fiber-optical communication networks.

As you can see, we can also use units from the electric realm to measure how loud an audio signal is. We will choose the most convenient unit depending on the context. Ideally, when using decibels, the type should be stated although sometimes it has to be inferred by the context.

If you read dB values on a mixer desk, for example, chances are they will be dBu, since this is the unit usually used in professional audio. When shopping for a pair of speakers or headphones, SPL values are usually given. Finally, when measuring things like an office space or a computer fan you will see dBA, dBB or dBC. These units are virtually the same as dBSPL but they apply different weighting filters that account for how we are more sensitive to certain frequencies than others in order to get a more accurate result.

And that's all folks. I left several things out of this post because I wanted to keep it focused on the basics. The decibel has some more mysteries to unravel but I'll leave that for a future post. In the meantime, here are some bullet points to refresh you on what you've learned:

Takeaways

The decibel:

  • Uses the logarithmic scale which works very well when displaying a wide range of values.
  • Is a comparative unit that always uses the ratio between a measured value and a reference value.
  • Can be used with any physical property, not only sound pressure.
  • Uses handy reference values so the numbers we manage are more meaningful.
  • Comes in many different flavours depending on the property measured and the reference value.