What is The Decibel | Amplitude and Dynamic Range.
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So far we’ve discussed what frequencies are and their different characteristics. We’ve also covered Harmonics and how the overlapping of different frequencies can cause waveforms to take different shapes (sine, triangle, square, and saw) based on superposition and phase cancelation, otherwise known as Constructive and destructive interference.
Today we’ll be looking deeper into Amplitude and how we measure it. We are already familiar with the positive and negative amplitudes of a frequency. But how do we actually calculate the amplitude of a wave? So that we can understand this at its fundamental level, we’ll be looking deeper into the Decibel and the measurements of loudness and what that has to do with Dynamic Range.
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Dynamic range is a huge buzz word in the audio industry. We’ll hear people talk about dynamics and whether a song or a piece of work has a wide dynamic range, or if it’s even dynamic at all. We’ll demystify this topic today.
In order for us to understand dynamic range, we’ll need to understand Amplitude more. We briefly learned about Amplitude in our very first lesson (What are frequencies). We learned that wave cycles have both a positive and a negative amplitude, and that the higher the amplitude the louder the sound. But how exactly do we measure how loud something is?
- Thanks to a guy named Alexander Graham Bell, the dB, or the Decibel, was created as an arbitrary way to measure sound. That's right, I said the dB is actually an arbitrary measurement.
Though there are over 8 different variations of the dB measurements, we’ll only be looking at 3 different versions of the dB. These 3 tend to be the most common and tend to be the most useful relative to the equipment we use in today's world of audio.
dB-SPL
SPL stands for “Sound Pressure Level” and measures the pressure variations in the air that are caused by sound waves. Sound pressure is measured in Pascals (Pa) named after French Mathematician and physicist, Blaise Pascal.
Just like Humans can only hear from 20Hz-20kHz (low to high pitch) the threshold of human hearing starts at 0.00002 Pa. Meaning the quietest sound a human can hear is 0.00002Pa. For reference, 0 pascal would be a perfect vacuum, or space. But unlike how we lose the ability to hear frequencies once they become too high pitched. There is no such thing as a ceiling to how loud something can be.
If we move upwards in Pascals (Pa), the threshold pressure level that Humans begin to feel physical pain is 20 Pa. For example, at 20 Pa, it only takes 7.5 seconds to cause irreversible damage to your hearing. If you were to experience 200 Pa, instantaneous hearing damage can occur (scary).
If you notice, we went from 0.00002 Pa all the way to 20 Pa. That is a massive difference between the threshold of human hearing and the threshold of physical pain
(1,000,000 values to be exact). This is where the Decibel (dB) comes into play. The dB is actually a Logarithmic equation that both reduces the distance between the threshold of hearing and the threshold of pain, and gives humans easier numbers to use as a reference guide when discussing sound pressure.
You don't need to memorize this equation, but I'm going to walk through it in order to give you a better understanding of the dB and how it's an arbitrary measurement.
dB-SPL = 20log10 (P/Pref)
Where P is the measured pressure in the room, and Pref (reference Pressure) is always 0.00002Pa which is the threshold of human hearing. That number then gets multiplied by the 20log10 which then allows us to convert Pascals into dB!
Here are the example problems using the threshold of human hearing and the threshold of pain.
20log10 (0.00002 / 0.00002) = 0 dB-SPL - threshold of human hearing
20log10 (20 / 0.00002) = 120 dB-SPL - Threshold of physical pain
(Damage after 7.5 seconds of exposure)
Instead of counting from 0.00002 to 20 (essentially counting to 1,000,000) we now only have to count to 120!
Even better yet, we’re not supposed to be around 100dB-SPL for more than 15 minutes because of potential damage to our hearing. So typically we will only work with 0-100 dB-SPL. Anything over requires ear protection!
So What is dB-SPL? It's the way to measure the variations in air pressure caused by sound waves.
dB-V / dB-u
The V in dB-V stands for Voltage! Hold on a second, when did we go from air pressure to electricity? Good catch! Remember when I said that the decibel is an arbitrary measurement? A better definition is “the decibel is a ratio between two powers” whether it's in Voltage or as Air pressure. I know I said we were going to cover 3 variations of the dB, but dBu will be the secret 4th and for good reason.
dBV = 20log10 (V/Vref) where the reference Voltage is exactly 1 Volt
dBu = 20log10 (V/Vref) where the reference Voltage is 0.775 Volt
0dBV = 1v and 0dBu = 0.775v
dBu was the initial standard for measurements for electrical audio signals when the phone lines came out in the mid-20th century.
dBV became standardized after consumer audio equipment started to become popular and some electrical engineer was so sick of using 0.775 Volts for all of his equations and ended up just rounding it to 1 Volt. The dBV then became a friendlier standard for Consumer grade audio products.
What's the difference between consumer and professional audio equipment?
Take a look Look at this surround sound unit for a home theater system. This is a consumer grade audio product. Consumer Line level is -10 dBV or 0.316 Volts. This is also the same audio signal that will come out of your phone and into your headphones, same as the Aux cable from the headunit in the car, or a DVD player plugged into the TV. The -10dBV standard means the device should be able to handle -10dBV without any issues. How much it can handle over that though, is dependent on the manufacturer and their individual standards.
Now look at this mixing console. This mixer uses Professional Line Level. Which is 0dBV or 1 volt. But you won't actually see dBV on most professional gear. What we will see a lot of though, is +4dBu (1.23V). This is because the professional standard stuck with dBu even after the consumer standard changed to dBV!
dBu = dBV + 2.2, Or in other words, 0 dBu is equal to -2.22 dBV.
When working with professional audio equipment you’ll notice there are typically two options given, Mic and Line.
A microphone converts sound waves into electrical signals. A microphone can typically produce an electrical voltage from around 0.001 up to 0.01 Volts. In other words -57 to -37dBu. And a Line signal is typically considered a standard operating level.
So while Mic level is around -60 to -40 dBu or 0.001 Volts.
Line level is +4dBu / 1.23 Volts.
Side note: (this is why Microphones need a “Preamp”, to get the mic level up to line level).
Consumer Line Level is -10 dBV or 0.316 Volts.
Professional Line Level is +4dBu or 1.23 Volts (or 0dBV).
Professional Mic Level is -60 to -40dBu or about 0.001 - 0.01 Volts.
Distributed speaker systems using power amplifiers can be measured up to 100 Volts or 40dBV.
This makes entire measurable range in dBV / dBu is -60 to +40dBV with 0dBV being roughly in the middle.
So what are dBV & dBu? They’re measurements of Electrical signals produced by analog audio equipment. With dBV being a consumer grade measurement and dBu being a professional grade measurement. Same same but different.
dBFS
Also known as dB Full Scale. This will be the most common measurement of dB’s when it comes to Digital Audio. Unlike its analog counterpart the dBu, which can range from -60 to +40dBu. dBFS has a maximum level of 0dB! Anything over 0dBFS will distort or “clip” the audio. We’ll get into that in a later lesson.
The dBFS is probably going to be one of the most important dB measurements you’ll use in audio production and engineering. This will be the primary measurement when working with audio software on a computer, or a digital recording console. This is the “dB” the majority of people are talking about when generally speaking of audio.
Looking at analog mixing consoles, you’ll see a lot of VU meters which are calibrated to measure in dBu!
When recording music with a computer, we move from the analog world, to the Digital world. In the digital world or dBFS, our entire measurable scale is from -100 to 0dBFS.
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IMPORTANT: Most audio softwares and digital consoles use dBFS, but will simply be stated as dB. dBFS will be dB unless specifically indicated otherwise.
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Instead of looking at dBFS as a physical measurement of Air Pressure or Electrical Voltage. dBFS is simply a computer's way of displaying its maximum digital level. Anything more than its maximum digital level and we start to create digital artifacts and destroy the audio the further we push it past 0dB. The equation for dBFS utilizes Bit depth information to find the ref values, this is something we’ll get into later with a full lesson dedicated to it.
So what is dBFS? dBFS is a Digital scale that indicates the Maximum Digital Level a computer or digital console is able to reproduce. It is more often referred to as just dB, and it’s scale is measured from -100dB being the lowest level, to 0dB being the absolute Maximum level and is the primary dB measurement in digital audio applications.
- The important thing to know about the decibel, is that it's a ratio between 2 powers. It's a logarithmic scale that simplifies complex equations in order to give us a more simple and human friendly explanation of what's going on with audio around us.
dBSPL is used for sound pressure / 0 to 120+ dBSPL
dBV and dBu are used for Electrical Voltage / -60 to +40dBV
dBFS or dB is used for Digital Audio work on computers / -100 to 0dB.
Look at that… we made it out alive! We just covered a lot of numbers but it’s good for you! If you’ve made this far in our lesson series, you know more about the fundamental principles of audio than most people. Keep it up!
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Amplitude
So, in our first lesson when we learned about frequencies. We discussed how every cycle of a frequency has a positive amplitude and a negative amplitude. To keep it simple, the higher the measured dB, the greater the amplitude, regardless of what variation of the dB you’re using. Whether it’s in SPL, dBV, dBu, or dBFS.
Examples:
A quiet room with no one talking would sit around 40dBSPL. If I were to measure myself whispering in my closet, it would be somewhere around 45 to 55 dBSPL. Where as the average rock concert sits at a loud 90-120dBSPL.
You could say that my whispering has a low amplitude compared to the rock concert’s high amplitude.
Another example of a low amplitude sound is someone tapping a pen on a table.
A high amplitude sound would be an airplane taking off.
A low dB measurement is a low amplitude and a high dB measurement is a high amplitude, regardless of what variation of the dB you’re using. Whether it's SPL, dBFS, or dBu.
Low amplitude is quiet, and high amplitude is loud. A low Amplitude is a low pressure change, while a high amplitude is a high pressure change. A low pressure change is a low dB measurement. A high pressure change is a high dB measurement.
Easy enough right?
- Don't worry, all the brain melting learning was early in this lesson but for good reason! If you understand the correlation between amplitude and dB, getting into the topic of Dynamic Range will be easy to grab ahold of.
Dynamic Range / Dynamics
Dynamics, or Dynamic Range is the relative distance between multiple dB measurements, regardless of the variation of dB measurement you use.
Examples:
If someone is talking around 60 dBSPL and a Rock concert is around 120 dBSPL. There is a total dynamic Range of 60 dBSPL between them.
If the computer's dB meter says channel one is at -30dB, and channel two is at -10dB. There is a total dynamic range of 20dB between them.
Imagine this scenario, we are at a studio and recording a band on an analog mixing console. While we watched the VU meters, we noticed at the beginning of the song when it's just the singer singing acapella, the VU meter stayed around -15dBu. Once the rest of the band starts playing we watch the VU meter jump all the way up to +2dBu. This would indicate that there is 17dBu of dynamic range from the quietest part of the song to the loudest part of the song.
Dynamic Range is the difference between the quietest and the loudest sounds whether it’s naturally occurring in nature, sounds on a digital recording, or the difference in voltage readings between an electric guitar vs a keyboard.
The greater the distance between measurements, the greater the dynamic range. The smaller the difference, the less dynamic range there is.
So what is Dynamic Range? It's the difference between the lowest amplitude and the highest amplitude sounds and is measured in dB. The greater the difference in amplitude, the wider the dynamic range. The closer the amplitudes are, the less dynamic range there is.
- Feel free to leave a comment or a question down below, I’m more than happy to answer specific questions!