6.3 Sound

Critical Questions:

  • What is a sound wave?
  • How do we hear sounds?
  • How do multiple sound sources mix together to form one sound signal?
  • Why does a flute sound different than a piano?

The well-known Zen koan asks: if a tree falls in the forest, does it make a sound? If you’re ok with the idea of not reaching enlightenment just now, physics can give a rather bland answer to the question.

Thinkin' real hard about physics right now
Thinkin’ real hard about physics right now [source]
Sound is nothing more than vibrating air. When you speak, for example, your vocal cords are moving rapidly back and forth, striking air molecules with every forward motion. These first few molecules rush forwards until they run into other molecules, at which point they collide and move back, repeating the cycle. This vibration spreads and moves through the air as a wave, causing molecules in all directions to begin vibrating. At some point, the air near someone else’s ear might vibrate as well, and the wave will travel the short distance down the ear canal until it reaches the eardrum (or ‘tympanic membrane’, which sounds much more official).

The tympanic membrane stretches across the ear canal like the skin of a drum. When it vibrates, it causes a very small bone inside the ear to vibrate as well, which then pushes another bone, which makes the fluid inside a strange, spiral-shaped hollow space begin to vibrate. The oscillation of this fluid jostles some tiny hairs at the same rhythm, and here’s the best part: every time one of these hairs bends, it sets off a small chemical trigger which sends a message to the brain. The brain then interprets the timing of these signals – their intensity and frequency – and translates that information into sound.

So, in short, yes – a falling tree does make a sound. Even if nobody’s around to receive those sound waves and interpret them, the waves themselves still exist.

The intensity of a sound is the distance it causes air particles to move in their vibrations, and it’s interpreted by the brain as loudness. Frequency is measured as the number of vibrations per second, so that air that’s vibrating more quickly has a high frequency. Our brain interprets sound frequency as pitch: a higher-frequency wave sounds like a higher-pitched note.

Because the tympanic membrane can only bounce in one dimension (in and out), and because those little hairs can only bend back and forth, all sounds – even the most complex ones, like Liam Neeson shouting something while a nearby building explodes on top of a tense, symphonic soundtrack – consist of a very limited signal. I already alluded to this during the introduction, where we saw that a musical recording with multiple instruments and vocalists can still be reduced to a simple waveform.

After writing this paragraph, I googled "Liam Neeson explosion". This was the first result. [source]
After writing this paragraph, I googled “Liam Neeson explosion”. This was the first result. [source]
In order to understand how multiple sounds can all exist in one signal, we first have to understand what happens when two waves meet.

This is another simple experiment that can be performed wherever you have access to some still water. Make two gentle waves and watch what happens when the ripples meet. The most obvious result will be that each wave passes right through the other and continues on. But if you look very closely, you might see the more important point: at certain spots, the water will bulge up twice as high as before.

This phenomenon is called interference. It is fairly easy to understand if you’re thinking of waves as the motions of interconnected molecules – if a particle is being affected by two waves, it’ll get pulled twice as much.

Now imagine two sources of sound waves – say, two nearby speakers playing two different notes. What you hear is not quite so simple as the two notes jammed together. Instead, you hear them both at the same time. This means that the air molecules reaching your ear must somehow be vibrating with two frequencies at once. This can be difficult to imagine, but it might look something like this:

Two waves interfering.
Two waves mixing it up [source]
In the diagram above, the lines would represent the motions of air particles. The bottom image represents what would happen when the top two waves “interfere” with each other. As you can see, the result is neither one nor the other, but retains some characteristics of both of the initial waves. This is exactly how sounds add up to produce one resultant waveform that reaches your ears as a complex sound.

It still boggles my mind to think about this, but the human brain is extraordinarily adept at picking apart complicated waveforms and considering them as combinations of individual sounds. The diagram above doesn’t do this phenomenon justice – it shows only two very simple waves. Real-life sounds are never that simple: they’re messy things created by oddly-shaped vibrating objects, they interfere with their own echoes and reverberations, and they pile up on top of all the other sounds coming from nearby. (If you want to keep thinking about this and saying “whoooooaa”, you should re-read the introduction to this chapter.)

But our brains have this insane ability to pick apart all of the sounds within a given wave, discard some of them, focus on others, and make sense of what’s left. It takes us some time to learn how to do this, of course, which helps explain the startled and confused looks on babies’ faces, but we get the hang of this seemingly impossible task relatively quickly. If too many sound sources mix, however, the resulting wave will be too complex to make any sense of – i.e, noise.

As you may have already figured out, interference determines another characteristic of sound, called ‘timbre’ or ‘richness’. A rich sound is made up of multiple sound waves, while a pure tone is one simple sinusoidal wave. This difference in timbre explains why you can distinguish between the sounds of a flute and a piano playing the same note (or frequency) – the waves resonate within the two different instruments to produce two different characteristic timbres. Your brain can interpret the same overall frequency from each one, but it also hears all of the other wave shapes that added up to produce the final sound.

I’ve thrown around the idea of “resonance” a couple of times in this post. Next time, we’ll figure out what resonance is, and how it could force a man to risk his life to save his dog from a collapsing bridge.

Big Ideas:

  • A sound wave is created when air molecules are made to vibrate. These vibrations spread out in all directions from the source.
  • The two most important parts of the human ear are the eardrum, which vibrates at the same frequency as the air hitting it, and the tiny hairs inside the ear, which transmit information about those vibrations to the brain by bending at the same rhythm.
  • Waves mix together through a phenomenon called interference, whereby two waveforms can add up to create a third with characteristics of both.