Let’s Get Wavy

What exactly is sound? The Oxford Dictionary defines it as “Vibrations that travel through the air or another medium and can be heard when they reach a person’s or animal’s ear.” Which begs the question – if a tree falls in a forest but no one is there to hear it when it hits the floor, does it make a sound? Ok, this isn’t supposed to be a blog entry to stir up philosophical debates about what does and doesn’t constitute sound, I just couldn’t resist throwing in that old brain teaser.

What I want to go through in this post are some fundamentals about what sound is, the way it is commonly represented in the audio engineering world and how a basic understanding of the features of different types of sound waves can help you with your tone crafting abilities, both in the analogue and digital synthesis world.

What Does a Sound Look Like?

At first glance, this might seem like a bit of a strange question. You hear sound, right? Another way we can define sound is as the perception by a receptor (e.g. your sense of hearing) of a signal that has been generated by a source (e.g. you excellently shredding licks on your new axe). But what’s going on in between the source and the receptor?

For the signal to be transferred something needs to happen, and in the case of sound, that is by the transmission of a vibration through an elastic medium. An elastic medium can be anything that has molecules capable of vibrating. So that means air, plastic, water, even concrete! Now all we need to be able to look at sound is to create a display of those tiny vibrating molecules. Maybe something like this:

moving-molecules-2

Maybe not! The more conventional approach is to plot sound as waves on an x / y diagram, with time on the x-axis and amplitude on the y-axis. Sounds transmitted as electrical signals (i.e. the output from your electric guitar or a microphone) or translated into digital (i.e. in your DAW) can easily be visualised using an oscilloscope or in your DAW through a wave form visualisation plugin.

philips-PM3267-oscilloscope
A Philips PM3267 oscilloscope

Now that you can see the sounds you’re creating, the next step is understanding what exactly it is that you are seeing and more importantly, how this translates into what you can hear.

Simple vs Complex

You’ve plugged your bass into your ADC, set your input gain levels nicely, armed a track to record and added your newly downloaded free wave form visualisation plugin to the channel strip in your DAW so you can analyse the wave form. You twang an open A string and this is what you see…

bass-A-smartelectronix-clean

“Er… what!? How am I supposed to make sense of this?” you may be asking yourself. A fair question and honestly, one that I don’t think you need to worry yourself with right now. What you are seeing is an example of a complex wave, that is a sound wave made up of a fundamental frequency (55 Hz in the case of a low A on a standard 4-string electric bass) and overtones. Overtones can be harmonic (exact multiples of the fundamental frequency – 110 Hz, 165 Hz, 220 Hz etc…) or inharmonic (all the frequencies in between).

The French mathematician and physicist Joseph Fourier showed through his analysis that all complex waves (except those generated by transients – a discussion for another day) can be broken down into a series of simple waves.

A simple wave is the wave form displayed when a single frequency containing no overtones is played. Whilst this sound is effectively non-existent in the natural world, thanks to the wonders of technology we can create this using a sine wave generator. The smooth periodic oscillation of a sine wave is the simplest wave form and the building block for all others.

Features of a Wave

Using the example of our trusty sine wave (remember them from trigonometry classes?) we can define a few fundamental features of a wave.

sine-wave

Amplitude – The strength of the wave signal, perceived by the human ear as the signal’s loudness. Commonly displayed on the y-axis of an oscilloscope.

Wavelength – The distance the sound wave is required to travel to complete one full cycle (i.e. the distance between each crest or trough)

Frequency – How many cycles of the wave are completed in one second, measured in Hz (hertz – named after German physicist Heinrich Hertz)

Phase – The position at a point in time during a wave form cycle (e.g. the crest and trough in the above diagram)

Period – The time required for a repeating wave form to complete one full cycle

Now that we know the basics, we can start adding multiple waves together to discover what sounds we can create, both visually and sonically.

Other Wave Forms

If you’ve ever dabbled with synthesis, you’ve probably encountered a few other wave forms. Let’s delve a little deeper into those and how they can (in theory) be constructed using nothing more than a combination of sine waves.

Square – By adding odd harmonics (i.e. 3rd, 5th, 7th etc.), each of declining amplitude, to a given fundamental frequency, we get a square wave, aptly named because on an oscilloscope you get, well a series of squares (or more likely a rectangle) represented above and below the zero-amplitude line.

Sonically, square waves have a thick, rich, raspy texture. Sound like any effects you know? In theory you can create your own using multiple sine wave generators set up at odd multiples of a fundamental.

Taking our example of a low A on a bass, this would be the fundamental at 55 Hz plus the odd harmonics 165 Hz (3 x 55), 275 Hz (5 x 55), 385 Hz (7 x 55) … you get the idea. It’s easier described than executed in practice, so if you want a pure square wave, just flip your wave generator to the square wave setting and you’ll be golden.

Triangle – These are constructed exactly the same as square waves (odd harmonics of a fundamental), it’s just the amplitude of the harmonics are half as strong as with a square wave.

Sonically a triangle wave is less harsh than a square, as the wave form is heading back in the direction of a sine wave.

Sawtooth – This one adds back the even harmonics (2nd, 4th, 6th etc.) so you get the fundamental plus all odd and even harmonics.

Sonically a sawtooth is much brighter, in your face and loud that the other wave forms.

waveforms

What next?

Now that you’ve got your head round some of the basics of how audio can be represented, I’m sure you’re itching to put this to good use. The waves we’ve described above are by no means all encompassing. In fact, all of them are quite artificial and you’re not very likely to be able to create exact replicas using pure analogue sources. However, a solid understanding of the concepts described and the key features of these common wave forms will stand you in good stead in your ongoing journey of tone discovery.

Before we open the lid on the audio theory behind some of your favourite tone shaping effects, we want you to go have a play and see if you work out the kind of waves that are being created when you plug into your favourite pedal (just what exactly is happening inside that new Klon Centura you’ve purchased that delivers that killer overdrive sound?).

Have some fun playing around with your effects boxes and be sure to check back in a few weeks when we’ll be delving into the world of gain, modulation, frequency and time-based effects. All of which can be broken down and understood using the basics we’ve outlined in this post. Now that’s wavy*!

* The new futuristic way of describing something in a positive connotation, popularised by rapper Max B (https://www.urbandictionary.com/define.php?term=wavy)

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