Coffee

Mathematician explains resonant frequencies and how not to spill coffee

Since sound is a wave, there are, uh, resonances between audio and fluid dynamics. And that brings us to playground swings and how not to spill your coffee. Let’s let Oxford PhD math student Sophie Abrahams explain the research done by original author Jiwon Han.

This video is a great introduction to resonant frequencies, as the playground swing metaphor would work well for sound physics beginners.* Not that I need to make that kind of link, of course – without coffee, frankly, most musical instrument technology would grind to a halt. (I swear I do not mean to keep hitting these dad puns.)

We also discover the natural frequency of a standard cylindrical mug – just the thing if you want to tune an LFO to your mug’s frequency.** Move over, 432Hz! Firstly, that’s totally not the frequency of the universe. Secondly, my coffee mug is my universe. Solved.

The whole paper is a fantastic read, which earned it a Fluid Mechanics IgNobel Award in 2017.

Han, J. (2016). A Study on the Coffee Spilling Phenomena in the Low Impulse Regime. Achievements in the Life Sciences, 10(1), 87-101. https://doi.org/10.1016/j.als.2016.05.009

To back up and see a really basic introduction to resonance using flames, there’s this:

Speaking of which, you know that “glass-breaking” thing? (It’s a film/TV trope, too, usually involving a mezzo-soprano screaming a high note.) It’s real. Even the singers. I hit some resonant frequency in a DJ set in Milano in November and broke a lightbulb. (The venue didn’t typically host sound.) I was playing normally; it was resonant frequency. I’ll deploy a material scientist if they send me a bill, I guess.

Here’s the example with a voice, with some great slow-mo footage – and think back to the swings example, as you already know how to do this pushing a swing:

So the part that’s a myth is that this requires a high, loud voice and… Viking horns. But now you know it’s just a matter of matching the voice to the glass. That could explain why this documentary, based on the incorrect assumption (high pitch, extreme loudness) took 139 takes to get right. You should pay attention in physics class after all:

Now, liquid oscillation involves fluid dynamics, which we really don’t think about in sound work, but the property of resonant frequencies is connected. In fact, you can work in the other direction. Physicists have modeled resonant frequencies in fluids to study distant neutron stars – and there you involve quantum physics.

If that sounds really complex and something only an astrophysicist would follow, you’re right. But it does work out to building what amounts to a model of the star with gas in a lab and then running a filter sweep through it, literally the same way you test a room. Seriously. It’s like room calibration meets that school science fair volcano project, only under lab conditions and you’re precise enough to be predictively calculating quantum friction.

Physicists capture the sound of a “perfect” fluid [MIT News]

This is the sweep they use. Sound is sound – even in astrophysics:

And are you thinking what I’m thinking? It’s the 2020s, and we’re one step closer to literally creating something like the Brownian Motion detector Douglas Adams inserted in a cup of tea as a punchline while envisioning the Infinite Improbability Drive. (Okay, granted, not exactly, but still hilariously closer than I’m sure Adams would have imagined.) Just swap that tea for some strong coffee.

I have really just one gripe in this article, and that’s – Sophie! This could be Dr. Sophie by now, since the video isn’t new. After all that, you’re just going to use a lid?? What are you doing?!? Sheesh, I will absolutely be using the claw grip now; the paper even has a great graph on how it works. And occasionally impressing people by walking backward. If this doesn’t sum up the difference between theoretical and applied research, nothing does. Disappointing.

*/** There is some chance that I wrote this entire story as part of a running coffee obsession I have with Artemiy. Good morning.

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