Science In Real Life

You’re tooling down the highway blasting Britney Spears’ latest comeback attempt. You’re in the supermarket, hearing the latest update on that cleanup in aisle four. You’re watching the pundits on TV attempt to offer intelligent commentary. In a meeting at work, everything stops while that jerk from Accounts (you know the one) fumbles to shut off the irritating ringtone of his wife calling for the third time that day. What do all these scenarios have in common? You are hearing a complex pattern of sounds produced by an electronic device. How does that happen? The science of turning electricity into sound is called electroacoustic transduction, and it can be accomplished by a variety of setups. I’ll focus here on the two most common, a basic loudspeaker and piezoelectric devices. If you’re good there will be a surprise at the end.

First, recall that a single-toned sound wave is a repeated pattern of compression and rarefaction of the molecules of air (or any other substance). That alternating pressure front pushes on your eardrum with a regular frequency, which your brain interprets as sound. Complex sound patterns, like that song that’s been stuck in your head all week, are fundamentally the same but with more variation in the pattern. So if we want to produce one, we need a device that can vibrate the air over a wide range of frequencies, and we need to be able to control exactly what the frequency is at any given time.

Let’s start simple. How do we vibrate air using electricity? Enter the loudspeaker. The basic design is this: A permanent magnet sits next to a coil of wire. The coil is in the shape of a cone, and it sits on top of a bigger cone made of a flexible diaphragm. When electric current runs through the coil like curry through an American, it generates its own magnetic field (see here), and presto! The coil repels from (or attracts to) the magnet, pushing the diaphragm. If I give the coil a little bit of current sixty times per second, the diaphragm vibrates the air sixty times per second, creating a sound wave of frequency 60 Hz.

It may not be immediately obvious that this setup is capable of generating truly complex sound patterns, which can have dozens of different frequencies overlapping (all at different amplitudes). In fact it is no bother at all. Imagine first that the diaphragm, when it pulses, does so in no time at all (this is not so far from the truth). I put a 60 Hz tone in. What’s the diaphragm doing in between those pulses? Nothing. It’s free to generate a pulse for a tone of a different frequency. So our speaker can generate simultaneous frequencies as easily as a chessmaster plays multiple games.

Of course, to get to something recognizable as speech we have to truly ramp up the complexity of the waveform, but the underlying principle has not changed: all waveforms, no matter how complex, can be approximated by adding up a sequence of single-frequency waves. (Advanced note: This is called a Fourier series. Decomposing a waveform into its component frequencies is called a Fourier transform.)

Next up we have piezoelectric speakers. Sure, the loudspeaker is great for crowd control, or making sure the entire neighborhood knows your car has a sound system, but in today’s modern world of tiny electronic devices, we need something smaller and more precise. Perhaps something that can produce sound at a molecular level. The simplest piezoelectric substances are crystals, which, you’ll recall from the very first essay, are rigid lattices of oppositely charged atoms. When I apply a voltage across the crystal, it pulls the positive atoms one way and the negative atoms the other. Unless the geometry of the crystal prevents it, the atoms will all actually move to each side — pulled in two directions at once like a suburban mom on a Tuesday afternoon.

What that means is, the crystal elongates along the direction of the voltage. Picture a flat square plate made of piezoelectric crystal sitting on a table. It has some thickness rising up from the table. If I apply a voltage along the surface of the table, the piezoelectric square becomes a piezoelectric rectangle, and gets thinner in the third dimension. Turn off the voltage, and we once again have a square of its former thickness. Repeat ad nauseum at a suitable frequency, and the square will vibrate the air at that same frequency by adjusting its waistline back and forth faster than someone hooked on fad diets.

Making the piezoelectric speaker roughly pancake-shaped is important. The change in width is very tiny; as the crystal gets thinner, more of the vibration is absorbed by the air and less by the mass of the crystal itself. Then, adding surface area allows the crystal to vibrate more air, creating a more intense sound, like adding more babies to a maternity ward. Piezoelectric speakers, compared to loudspeakers, are more compact, quieter, and are more precise at high frequences. Conversely, the larger loudspeakers are the thing to use for low frequencies and are, as their name suggests, quite loud.

Interestingly, crystals are not the only piezoelectric substances. Certain ceramics and polymers, despite lacking the rigid lattice, have a molecular geometry suitable for generating material stress under the separation of opposite charges. Several organic substances are also piezoelectric, including silk, human tendons, bone, and enamel. Chew on that.

Now, you’ve all been very attentive through this unusually long essay, so here’s a treat. One other way to generate sound is by repeatedly exploding the air with giant electric sparks, as in this video of two giant Tesla coils playing the Mario Brothers theme: