Resonance Frequency… of Walking!

This summer I had the distinct privilege of participating in an internship for the Society of Physics Students and the American Institute of Physics. I’m working with the American Physical Society (APS) in their Outreach department, on a (VERY VERY COOL) project called “PhysicsQuest“.

I’ll expand on PhysicsQuest and why it’s so awesomely cool in a separate post (which it deserves). For now, I want to discuss a rather amusing incident that happened the other day at the office.

Something’s Fishy

I had some work to finish and I decided to stay late. As I was working on my extension activities and trying to devise physics experiments to do at home (familiar?) I noticed the team leader (and my internship mentor), Rebecca Thompson, carrying a fish tank, half full of water, out of the office and towards the kitchen.

Fish tank, Stationary

 

She was walking really really slowly, carrying the big tank with both hands carefully, and seemed to make an actual effort to walk steady. I turned and asked if I could help, thinking the tank must be extremely heavy, to which she replied with one of the best physics comments I heard to date:

“It’s not that heavy, but my walking pace matches the resonance frequency of the tank, so I just have to walk slowly.”

Ha! Brilliant! See, most people would simply state “If I walk too fast, water will splash all over me.” But that wouldn’t have been physically accurate, and Becky would have none of that. She stood firm to Physics – and explained it much better.

Resonance Frequency and Fish Tanks

Her explanation was, of course, absolutely right. The ‘usual’ explanation makes the connection between the splashing of the water to the speed of the walk, and that’s not entirely accurate. You could, theoretically, walk faster and still not get splashed, if you manage to walk at a steady pace, not hit anything, and avoid the resonance frequency.

Resonance-wha?

When an object oscillates back and forth steadily, we describe the movement as having a frequency. The frequency is the number of repetitions per certain amount of time. So if an object oscillates back and forth three times per second, we describe the movement as having that frequency of motion: Three oscillations per second (or 3 Hz).

When the fish tank is moved or shaken, the water inside it oscillates back and forth, creating a recurring wave that bounces from one wall of the tank to the other. This wave has a certain frequency, and assuming the walking pace of whoever carries it remains constant, the frequency remains more or less constant as well.

But frequencies also have this unique little phenomenon called “Resonance”. The wave inside the tank overlays itself. Most of the time, the overlaying waves would cancel a small bit of one another, keeping the water well inside the tank. But if the frequency is just right, the recurring waves build-up, and the amplitude (or, in this case, the height of the splashes) increases more and more and more and— you get soaked with fishwater.

Resonance Frequencies. Source: Wikipedia (http://en.wikipedia.org/wiki/Resonance)

For Becky, her normal walking pace creates vibrations that match the resonance frequency of that size of tank, causing the waves inside to increase and increase…. dangerously close to splashing her completely.

Changing the Walking Pace

There are two ways to avoid this resonance frequency – either vibrate the tank slower (as she did by walking slowly) or vibrate it faster. Of course, vibrating the tank faster than the resonance frequency would, in theory, prevent the waves from adding-up dangerously, but it carries the additional risk of either bumping into something (oops) or shaking the tank uncontrollably and having water splash on you regardless of frequencies.

She made the safer choice. And she remained dry. And completely physics’y!

Other Examples of Resonance Frequencies

Resonance frequencies aren’t just about water. They are relevant in many aspects of our lives, especially when new buildings and bridges are built. Whenever something vibrates your new construction, you need to be careful about resonance frequency. Even if your bridge is tough enough to sustain a large amount of weight on it, if the objects on it create vibrations that are exactly right (or, in this case, exactly wrong), you can have a serious problem.

There are a few examples of this actually happening in real life. I didn’t have a camera when Becky carried her fish tank, and I doubt she’d have agreed to a demonstration*, but there are a few videos online that show this principle in much larger scale.

The Tacoma Bridge Disaster

One example of resonance frequency gone bad is The Tacoma Bridge disaster. The original Tacoma Bridge was a suspension bridge built in 1940 in Washington state. It dramatically collapsed less than a year after it was opened.

On the morning of November 7th, 1940, winds were high across the bridge, reaching around 64 km/h (40 mph). This in and on itself probably wouldn’t have been enough to collapse the bridge, but the problem became much worse when the structure began oscillating back and forth like a pendulum. When one side of it would go up, the other went down, and repeated to the other side; this movement back and forth became more and more pronounced, as the bridge reached its resonance frequency.

httpv://www.youtube.com/watch?v=dm0XXuFt30k

As you can see in the video above, the Tacoma Bridge had these ‘swaying’ oscillations much before the disaster occurred. The day of the disaster, however, the oscillation frequency reached exactly that of the resonance frequency, and instead of remaining at a small amplitude, the vibrations increased until the bridge broke.

Here’s a great video summarizing the Tacoma Bridge disaster, including the physical explanation:

httpv://www.youtube.com/watch?v=3mclp9QmCGs

Walk Carefully

Theoretically, then, Becky could have simply run forward with the fish tank to avoid the resonance frequency. That probably would have resulted in shaking the water tank uncontrollably and having herself splashed anyways, so her choice was the best one.

Now, when you carry big containers of water, you can plan your walking pace accordingly! Does the water start splashing higher and higher? try walking at a steady pace, either faster or slower, and avoid the splashy power of the resonance frequency.

* Although it was, in all honesty, a very hot day, I doubt she’d want fishy water all over herself, even for physics’ sake.

Sources and More Info

Thanks

  • Amanda Palchak, for initial proof reading
  • Elizabeth Hook for finial proof reading
  • Mike Lucibella for taking my picture
  • Rebecca Thompson and the APS Outreach team for an awesome experience this summer!
    (And for this great physics quip)
2 comments
Paul
Paul

A similar thing happened to a footbridge across the River Thames in London 11 years ago: http://www.youtube.com/watch?v=eAXVa__XWZ8

The energy waves created by people walking on the bridge started to coincide and built up to the point where the bridge was unsafe to walk on. Engineers fitted dampers to the bride to effectively stop the problem. The media named it the wobbly bridge.

My house has resonance frequency problems from lorries passing on the main road close-by. The house shudders. The neighbour in the flat below me was convinced I had some machine in my flat that was shaking the whole house. It wasn't until one night he started banging on my door and I had to get up to tell him it wasn't me that he actually believed I didn't have an infamous house-shaking machine.

mooeypoo
mooeypoo

@Paul,

We have something like that in the office too, apparently. We're very close to the train tracks, and I was very surprised to see my desk trembling -- I thought it was an earthquake. But an earthquake in Washington DC doesn't make much sense. Apparently, whenever a big train passes by, the building shakes... we're at the right distance, and probably at the resonant frequency. Ha!

Physics

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