6.4 Resonance

Critical Questions:

  • What is resonance?
  • Can you shatter a wine glass just by singing at it?

In the same way that it must be illegal to talk about buoyancy without telling the story of Archimedes and the crown, everyone who teaches resonance brings up the Tacoma Narrows Bridge at one point or another.

This is probably because there is some cool old black-and-white footage of the bridge swaying and rippling impossibly in a stiff breeze, as follows:

It’s clear from the video that this was a windy day, but not tornado-windy. So what made the bridge move like that?

The best way to understand what happened to the bridge is to think of a swingset. Picture a happy little child sitting in the swing and demanding to be pushed. You pull them back a bit and then let go. What happens next?

If you like this child, you’ll wait until they’ve swung forwards and back before giving them another push. In other words, you’ll match up the frequency of your pushes with whatever frequency that particular swingset wants to be at. With each push, you’ll add to the child’s forward momentum, and they’ll swing higher and higher.

If you do not like this child, you might try pushing at a different frequency. In that case, you’ll find that most of your pushes won’t occur at the right part of the swing – sometimes you’ll even be pushing forwards while the child moves back. This kid won’t have a fun time. They’ll be jostled back and forth and will never get very high off the ground.

This is how one might push a young Joffrey Baratheon on a swing.
This is how one might push a young Joffrey Baratheon on a swing.

But when your pushes have the same frequency as the swing, we say that they are in resonance.

The main feature of resonance is that it results in vibrations of increasing energy, even if the force causing the vibrations isn’t very strong. You can get a pretty good swing going even with a relatively small push, as long as you keep pushing at the resonant frequency.

The engineers of the Tacoma Narrows Bridge certainly knew how to build something that would stretch over the river and not collapse under its own weight. What they didn’t know was that they had accidentally created a structure with a resonant frequency that would match the frequency of the wind on a fateful day in 1940. Each successive gust of wind tugged the bridge back and forth until the concrete began to ripple and the supports began to sway. Eventually, as you saw in the video, the whole thing just ripped itself apart.

Nowadays, bridge designs are always tested using scale models inside wind tunnels in order to make sure that the structure will not fall apart.

In truth, a bridge is much more complicated than a swing, and so its response to various frequencies is more complicated as well. It will most likely not have one simple resonant frequency that will cause it to vibrate so much that it breaks. Instead, it will have different responses to every possible frequency. The bridge engineer’s job is to design it in such a way that no one frequency elicits too strong a response.

Similarly, car companies employ people whose entire job is to test cars for resonance and make sure that the cars won’t start to make those annoying and mysterious buzzing sounds while driving down the highway. If a resonant frequency is found in a particular part of the car, the design will most likely be changed, sometimes using something as simple as an extra bit of metal to stop the piece from vibrating.

A wine glass, on the other hand, has a relatively simple structure. You can hear its resonant frequency just by flicking it with your finger and listening to the tone it makes. If you place the glass next to a speaker and play that exact frequency at a loud enough volume, the glass will wobble and eventually shatter. This wobbling is much too quick for you to see with the naked eye, but we can see it if we watch it through a slow-motion camera, as such:

It’s important to remember that it’s the frequency of the note and not the volume that breaks the glass. However, with the glass, the bridge, and the swing, we do need a minimum level of force for significant vibrations to result. This is because real-life objects lose some energy as they vibrate; energy needs to be added back in from an outside source in order to get vibrations of increasing size.

You might now be thinking of the busty opera singers from old cartoons, who could shatter windows just by singing a high note. This is not theoretically impossible, but it’s unlikely: due to the natural timbre of a human voice, it would be hard for her to hit a pure enough note to cause resonance. And she would have to be singing fairly close to the glass, because when noise spreads out after leaving a source, its energy spreads out as well, meaning that far-away windows would probably not break at all, and wine glasses on tables wouldn’t shatter unless their resonant frequency was the same as the windows, which is unlikely.

But I do heartily recommend that you spend a few hours tonight tapping wine glasses and then screaming at them in the same pitch. All in the name of science.

Big Ideas:

  • Most objects have one or more resonant or ‘natural’ frequencies.
  • If a strong enough force is applied to an object at its resonant frequency, the object will vibrate with increasing amplitude.