There’s a special little dance I have to  do between the coffee maker and my desk,   just to prevent my hot coffee from  spilling over the edge of the mug.

Maybe you’re familiar with it. The key is to walk smoothly, but not too  fast and also, for some reason, not too slow.

In the end, I often just give up and drink my  coffee standing in the middle of the hallway. Because no matter what I try, the  coffee is determined to slosh. And this doesn’t happen to a  lot of other beverages I carry!

So what’s going on? Turns out, it’s because of physics. Physicists love coffee, and they  love studying every-day problems.

Which means they’ve dedicated several   peer-reviewed papers to the  factors that jostle your joe. And it all comes down to an unlucky  connection between your pace,   the cup, and that tasty morning brew. [♪ INTRO] Beverages slosh when you walk  because of a thing called resonance. Think about sitting on a playground swing.

When you pump your legs, or if someone  pushes you with perfect timing,   then you’ll swing higher and higher. The cadence of that “just right”  timing is called a resonant frequency. In the case of the swing, it’s  determined by the length of the chains.

Any system that oscillates has these special  frequencies that can lead to resonance. If you add external force to the system,  and if it’s timed to match the resonant   frequency, then the amplitude of the  oscillations can become enormous. Did anyone else’s parents ever push  them to scary heights on the swing?

The story isn’t much different for  liquids sloshing around in a container. The resonant frequency of a liquid depends on  its density and the shape of the container. There’s a fancy formula that accounts for  all the details, and if you plug in a few   variables including the density of coffee  and the size of an average mug, you’ll find   that the lowest resonant frequency of the mug  is between 1 - 2.5 oscillations per second.

You can try this for yourself. Get a mug full of coffee, and  watch what happens as you walk. It might swish a little left and right,  as you switch weight between your legs.

But most of the sloshing is going to  be forward and backward, in line with   the direction you’re walking, and with a  frequency of 1 - 2.5 sloshes per second. Eventually these tiny motions add  together and end up making you spill. Because every time you take a step, you add  a force in the direction of your motion.

And here’s that unlucky connection  to your cup that I mentioned:   The average frequency of a person walking  is typically about 1 - 2.5 steps per second… That’s the exact resonant  frequency of a typical coffee mug! Those small forces, at just  the right time intervals,   make the waves in the mug get taller and taller… Until you’ve got a big stain on your khakis. Or in my case, my lab coat.

There are a couple tricks you could use  to make the ride smoother for your mug. And they all depend on disrupting that perfect   timing between your gait and  the mug’s resonant frequency. First, you can hold the rim of  the mug in a claw-like grip.

This alters how your body transfers  force to the mug as you step forward. The net effect is that you’re  less likely to hit resonance. But this grip introduces the risk of burning your  hand, plus you get finger grime all over the rim.

So another study suggests putting your coffee  mug in a little pouch suspended by long strings! As you walk, the pouch will  swing at a very different   frequency than the resonant frequency of the mug. Sooo I guess you could crochet a coffee mug sling!

Like, oh, let me just take a little  sip of coffee from my coffee purse. Or, my personal favorite, studies  suggest you could just walk backward,   which slows you down and makes your pace  irregular because… well because it’s weird. An irregular pace means that you can’t  jostle your mug at regular intervals,   which means no wave resonance.

But there are some obvious  problems with these solutions,   so let’s talk about some more realistic  ways we could prevent the sear of the slosh. Before we get into those solutions, a quick ad. Thank you for watching SciShow!

To keep videos like this  free for everyone forever,   you can join us in the second  annual Complexly Learnathon! Learnathon is a celebration of learning; of our  free content here at SciShow and all of Complexly. We’ve got new fun merch this month like scishow  dice, behind the scenes videos, and more.

Plus, a donor-exclusive discord where  you can play games and participate in   learning challenges with other Complexly viewers! Go to complexlylearnathon.com to check out the  Learnathon schedule and support our cool stuff! First, you could change your coffee order.

A layer of foam on top of a beverage  efficiently dissipates a lot of sloshing energy,   preventing large waves from building up  and eventually tipping over the edge. That’s why a pint of beer is far less  likely to slosh than a pint of cold brew. So consider swapping your  drip coffee for a cappuccino,   if you have a swanky office coffee bar.

Or, here’s an idea: We could just stop making mugs   shaped in the exact way that  causes resonance when we walk. Wine glasses and brandy snifters curve  inward at the top, and the change in   shape helps damp the oscillations that  make us spill from a cylindrical mug. The inward curve actually shifts the  entire shape of the oscillating wave,   so that even the tallest sloshes  are unlikely to spill out.

Mugs with a wide base and a narrow mouth  could solve these transportation issues! Why haven’t we done it yet? I guess cylindrical mugs are  easy to clean and drink from,   and they’re probably the  easiest shape to manufacture.

Pros and cons. But researchers suggest the best solution  might just be … paying attention. Now, I was a barista for many years,   and I was specifically told not to pay  attention to the coffee mugs I carried.

My trainers told me that paying too much attention  makes you overcorrect and ultimately spill more. Reddit is also full of tips for servers to  not look at the trays of drinks they carry. But one paper found that “focusing” on carrying a   mug can substantially reduce  the risk of coffee spillage.

They found the “focused” subjects  had smaller accelerations. Basically the coffee surface was still  pretty smooth by the time the subjects   got up to normal walking speed, aka  the mug’s resonant frequency speed. Smoother coffee equals fewer waves  that can get amplified at resonance.

So “focused” subjects were able to take  more steps before their coffee spilled. But that’s one paper against an entire  service industry’s worth of advice. I think we might need some more  studies on this particular point.

I know this all may seem trivial,   but these lessons do have some broader  applications, specifically for robotics. Motions like carrying a cup of coffee  require a lot of fine motor control. You, a human, can sense and respond to subtle   shifts in the motion of a  complex or chaotic system.

With practice and focus, humans  can balance weird shaped objects,   or carry mugs with chaotically-sloshing liquid. And there are many similarly complex tasks that  we’d eventually like to teach robots how to do. So researchers are studying how  humans carry cups of coffee,   trying to quantify their strategies for  predicting and controlling the system.

They’re applying these lessons to the ways that   robots adapt their motor control  in response to sensory feedback. So if you start seeing headlines about  coffee-carrying robots, you’ll know why. In the end, the best way to not spill  your coffee seems to be to take it easy!

Maybe sip your mug next to the coffee maker while  you gab with your coworkers about this video. Or switch up your mug-carrying grip to avoid  exciting the walking-pace resonance frequency. Gosh, can you imagine a  SciShow branded coffee sling?

As for me, I’ll be checking my local craft  markets for some unorthodox mug shapes. I’ll let you know if I find a good one. [♪ OUTRO]