Physics of Resonance: Tacoma Narrows Bridge Collapse

Instructor: Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

The Tacoma Narrows Bridge is famous for collapsing in a spectacular fashion during a windstorm. In this lesson, you'll dive into the physics of this collapse by learning about resonance frequency, and what that has to do with the bridge's downfall.

Galloping Gertie

We often take bridge construction and safety for granted. That is, perhaps, until we see one collapse before our eyes.

On July 1st, 1940, the Tacoma Narrows Bridge opened to the public in Washington. It was a suspension bridge that spanned Puget Sound's Tacoma Narrows Straight. This bridge was the third largest suspension bridge in the world for its time.

During construction the bridge had garnered the nickname 'Galloping Gertie' due to the way it swayed and bent in the wind. This wave-like swaying eventually became its downfall as the bridge collapsed on November 7th, 1940 during a windstorm; a mere four months after its construction was complete.

Galloping Gertie Bending in the Wind
galloping gertie bending in the wind

At the time, the Tacoma Narrows Bridge had been constructed to be the most flexible bridge ever built. So, how did a windstorm end up bringing the whole thing down? To understand that you need to know a bit about how resonance frequency and oscillators work, and that's what we'll learn about in this lesson.

Harmonic Motion

Before learning about resonance frequency, and what it has to do with the Tacoma Narrows Bridge disaster, we first need to understand something called harmonic motion. When you have an object oscillating back and forth periodically, we say it is experiencing harmonic motion.

One great example of an object experiencing harmonic motion is a free hanging spring with a mass attached to it. The mass causes the spring to stretch downwards, until eventually the spring contracts back upwards to return to its original shape. This process keeps repeating itself, and we say the spring is in harmonic motion.

Spring and mass in harmonic motion
harmonic motion

If you look at a video of the Tacoma Narrows Bridge, you can see that it was oscillating before it collapsed. Though the physics of a large structure oscillating are much more complex than the spring example, they both fall under the same basic concepts. It was undergoing harmonic motion just like a spring with a mass attached to it.

Damped and Driven Harmonic Motion

So far we've been focusing on the similarities between the oscillating of the Tacoma Narrows Bridge and the spring with a mass attached, but there is also one major difference between the two situations.

The spring with the mass attached eventually slows down and stops oscillating; however, this is not the case for the Tacoma Narrows Bridge. It just keeps oscillating in the wind until it literally shakes itself apart. The reason the spring stops and the bridge doesn't has to do with the type of harmonic motion they experience.

The spring with a mass attached to it is experiencing damped harmonic motion. A damped harmonic oscillator is one that constantly loses energy. In many cases this energy is lost due to friction, air resistance, or a combination of the two. This is the case for our spring, as it slowly loses energy to air resistance and friction until it stops oscillating all together.

Damped harmonic oscillator
damped harmonic oscillator

Instead of being damped, the Tacoma Narrows Bridge experienced driven harmonic motion. A driven harmonic oscillator is given energy by some external source. In the case of the Tacoma Narrows Bridge, it was the wind that was adding energy to it in order to keep it oscillating. Without the wind keeping it going the bridge would have been a damped oscillator, and eventually slowed down to a stop just like the spring.

Tacoma Narrows Bridge Collapse

Now, the day that the Tacoma Narrows Bridge collapsed wasn't the first day wind had caused it to oscillate - hence the nickname Galloping Gertie given to it before construction was even finished. So, what was different about the day the bridge shook itself apart? That day the wind happened to be continuously driving the bridge to oscillate at its natural frequency.

The Tacoma Narrows Bridge collapses
tacoma narrows bridge collapse

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