Complex Waves and Phase

Will Styler - LIGN 113

Today’s Plan

What are complex sounds?
What is interference?
What is ‘phase’?
How do we visualize and analyze complex sounds?

Last time, we talked about basic properties of sound

Amplitude, Duration, Period, Frequency and Wavelength
… and we ended with a sound that’s… not quite like the others

We’ve been looking at sine waves

Sounds which have just one frequency component
These are relatively rare in nature!
- It’s positively sineful that we’ve focused there
Most actual sources of sound generate multiple frequencies naturally

… and our ears (almost) never just hear one frequency

Because we’re surrounded by noise!
Noise arriving at the ear is additive
We only hear one waveform per ear, no matter the source(s)

So, we should probably talk about…

Complex Sounds

Sounds which are made up of more than one component frequency
Also, aperiodic sounds, which aren’t naturally derived from specific frequencies

We’re going to work with simplified complex sounds today

But the world is full of more complex complexity

How do we create complex sounds?

By making multiple sounds at the same time!
Or, mathematically, using addition!

Let’s look at this process in a bit more detail!

You can add very different frequencies!

Why would sounds be combined together using addition?

The sum of two waves is the sum of their pressures at any given point

Which gives rise to…

Interference

Multiple signals are ‘interfering’ with one another when they collide and affect one another
Affect means just that! Any effect at all!
There are two main kinds of interference in audio
- Constructive Interference
- Destructive Interference

Constructive Interference

When multiple waves combine in such a way that they become stronger
When peaks add together with peaks

Destructive Interference

When multiple waves combine in such a way that they become weaker
When peaks add together with valleys

Constructive Interference

Destructive Interference

… but wait

Those sounds had the same frequency
The same amplitude
… and the same duration
One pair combined constructively, and the other pair destructively
What’s the difference?

Phase

The point of the cycle in which a sound ‘starts’
The ‘orientation’ of the wave in time
We measure phase in Degrees (°)
- 0° is the base, and is the same as 360°
- 180° is the exact opposite phase from 0°

Phase is important for adding sounds together!

Sounds that are ‘in phase’ experience constructive interference
Sounds that are ‘out of phase’ experience destructive interference
- Also called ‘phase cancellation’ here

Constructive Interference

Destructive Interference/Phase Cancellation

Complete cancellation is relatively rare!

Phase effects aren’t all-or-nothing

Aside: Applied Phase Cancellation

Humans can’t detect phase

It doesn’t matter what phase a sound starts on to us
But it’s crucial when making complex sounds!

Subtle Phase differences matter!

Complex Sounds are everywhere!

How do we understand their components?

Using spectra or spectrograms
Using a Fourier Transform lets us understand the component frequencies and their phases
‘This signal is made up of which component signals?’

If you haven’t heard about spectrograms and spectra before, watch this video starting at 12:30

https://www.youtube.com/watch?v=59NqlXr59_c

This goes into a bit more detail (and allows me to be kind to the folks who’ve had 110 and/or 112)