X-Men: Series of Tubes

The new X-Men movie, X-Men: First Class, includes a mutant whose vocal powers let him shatter glass – as Charles Xavier explains, by matching the glass’s resonant frequency. Let’s look a little closer at resonant frequencies, and what they’re good for in speech (besides glass-breaking.)

But first, more glass-breaking.

Why does this happen? It’s not just the force of the sound wave smashing the glass – you could have two differently-shaped glasses, side by side, and one would break while the other wouldn’t.

If you tap a wineglass, it’ll vibrate, and you’ll hear it ring. The pitch of that ringing is the glass’s resonant frequency – it’s the frequency at which it naturally vibrates.

Now, setting aside wineglasses for a moment, imagine a kid in a swing. The swing, like any pendulum, goes back and forth at regular intervals – i.e., at a certain frequency. If you push them at the right moment when they’re going forward, they’ll swing higher. The frequency is the same – they’re going back and forth at the same rate – but there’s more energy in the swing. If you’re pushing at the right point in the swing, and if you push once in every cycle – in other words, you’re pushing at the same frequency that the kid’s swinging at – they’ll go higher and higher every time.

So if you play the wineglass’s resonant frequency, the wineglass, like the swing, will vibrate back and forth. The sound, like the adult lending a hand, gives a little push every cycle, increasing the strength of the wineglass’s vibrations every time. Get it vibrating intensely enough, and the glass goes to pieces.

The frequency needed will vary depending on the glass – this website had success with sounds in the 600 Hz range, which is a little more than an octave above Middle C. Plenty of singers can hit notes in that range – the real problem is hitting them loud enough. The sound needs to be 100 decibels or louder. Conversation is around 60 dB, and when you get up to 100 dB, you’re talking subway trains.

Caleb Landry Jones as Banshee in X-Men: First Class

Banshee in X-Men: First Class. Alien Tongues is in awe of his mutant cricothyroid muscle and his powerful phonation.

So when Banshee shatters glass, he needs to accurately match his pitch to its resonant frequency – and he also needs to increase his volume so he’s transmitting enough energy to shatter it and not just set it ringing. And those are just fragile little wineglasses. A big plate-glass window will require more oomph.

Human speech isn’t a series of single frequencies – if it was, you’d sound like a tuning fork. The vibrations produced by your vocal folds produce the frequency we’re most consciously aware of, causing your voice to be higher or lower in pitch. The other frequencies are produced by – you guessed it – resonant frequencies.

When people talk about the resonant frequencies of a tube, they aren’t talking about the frequencies that’ll make it shatter. They’re talking about frequencies that are amplified by that tube.

Imagine a tube that’s closed at both ends, with a speaker embedded in one end. When the speaker plays a note, it compresses the air in front of it. That wave of compression travels down the tube until it hits the closed end. Then it bounces back, creating a wave of compression traveling the opposite direction.

Eventually, it’ll bounce off the end with the speaker. If the speaker is compressing the air again, so a new wave of compression is coming out, the two waves add together and the sound is amplified.

As you can see, the timing has to be right for this to happen. If the wave of compressed air bounces back a little too early, or a little two late, the two won’t join together. Plus, those waves of high-pressure air alternate with waves of low-pressure air. (The amount of air in the tube doesn’t change, so if we push more air molecules into one part, there are fewer to go around elsewhere.) If the bounced-back wave of high pressure matches up with an outgoing wave of low pressure, the two will cancel each other out, making the sound softer, or damping it.

Whether the timing is right depends on the frequency of the sound, and the length of the tube. The first resonant frequency is the frequency whose wavelength is twice the tube’s length. Higher multiples of this frequency will also be amplified.

You get a similar effect if one end of the tube is open. The difference is that instead of bouncing off the closed end of the tube, the wave of high pressure bursts out into the surrounding air. Air molecules have left the tube, and a wave of low pressure goes bouncing back down towards the speaker. (Similarly, when waves of low pressure reach the open end, waves of high pressure rush back.) The overall effect is the same – some frequencies are amplified, and others are damped.

This is interesting to us because when you talk, your mouth is an open tube. And as you move your tongue and your lips, you’re changing the length of that tube. So you’re amplifying and damping various frequencies, resulting in the sounds of speech.

I am eagerly awaiting the next X-Men film, in which I hope we will see Banshee exploring the effects of different speech sounds on his powers, and using the particular frequency patterns of a well-timed nasal vowel to prevent the Kennedy assassination.

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