natural frequency

Natural frequency: The good, the bad and the catastrophic

What do bridge disasters and shattering wines glasses have in common? They’re both examples of what can happen when an object’s natural frequency is triggered by an outside force: In the case of the bridge, the wind; in the case of the glass, a powerful perfectly-pitched tone. Read on to understand more about natural frequency, mechanical resonance and resonance disasters.

It don’t mean a thing if it ain’t got that swing

When Duke Ellington composed this song, he didn’t just hit on a core truth of music. As it turns out, the physical universe is all about swing. That’s because all objects have what is known as a natural frequency. This is the frequency at which they begin to vibrate when a force is applied.

We can observe this phenomenon with a weight on a string. If we give it a little push, the weight swings back and forth at a certain speed. This is the object’s natural frequency which we can change by increasing the weight or altering the length of the string. Another good example is a wine glass. If you tap the wine glass with a fork, you’ll hear a tone emitted. The pitch of this tone is determined by the natural frequency of the glass. It will always vibrate at this frequency when set in motion by an outside force.

If the force applied to an object corresponds to the object’s natural frequency, the amplitude of this frequency will be enhanced. For instance, if the oscillating sound waves of an opera singer’s voice are the same as the natural frequency of a wine glass, the result will be an enhancement of the natural frequency — its amplitude will increase. Note that amplitude is the measure of the strength of an oscillation measured as the distance from the point of equilibrium.

This sounds complicated, but it’s actually quite intuitive in practice. The art of using an object’s natural frequency to enhance amplitude is something children figure out all the time using nothing more than trial and error. To set a swing in motion, children quickly learn to align their kicks with the swing’s natural frequency. In the case of a wine glass, the amplitude of the natural frequency can be increased to the point where the object can even break apart.

Catastrophic resonances

This is all very interesting with a wine glass, but enhancing the natural resonance of larger objects such as bridges and skyscrapers can lead to disaster. In fact, these disasters even have their own name: Resonance catastrophes. This is why engineers are careful to give their structures natural frequencies that are unlikely to be triggered by natural forces like strong winds and earthquakes.

A famous example is the 1940 collapse of the Tacoma Narrows Bridge in Washington State. Built in 1938, the Tacoma Narrows Bridge was the third longest suspension bridge in the United States but problems were apparent from the start. Strong winds caused the bridge to ripple like a wave to the extent that those working on the project dubbed it “Gallopin’ Gertie.” You can see the fate of the Tacoma Narrows Bridge in the following video:

We’re happy to report that no people died in this disaster, although an unfortunate dog that could not be coaxed from a car perished. The Tacoma Narrows Bridge is now a textbook case in how not to design a building or bridge. Engineers today take the resonant frequency of the objects they construct into account so that wind or other forces do not trigger sudden and catastrophic increases in amplitude.

Complementary resonances

With musical instruments and loudspeakers, an object’s natural frequency can be used to enhance sound. Acoustic guitars and violins, for instances use the natural frequency of the instrument’s wooden body as a mechanical amplifier. The odd pear-like shape of a typical guitar is constructed in such a way that a range of frequencies are amplified. Many subwoofers have bass reflex ports that help strengthen the system’s low end. Bass reflex ports, also called bass reflex vents, are long tubes that release air generated when a driver pushes back. They are specially constructed so that the air resonates within the cavity, a phenomenon known as the Helmholtz resonance, in such a way that the sound coming from the front of the driver is enhanced.

Loudspeaker resonances

Aside from bass refelx vents, however, most loudspeakers are designed so as to avoid triggering any of the natural resonance frequencies of the materials they are made from. For instance, the air pushed backwards into the enclosure by the driver could cause a poorly designed cabinet to resonate. The resonating of certain components at certain frequencies would be detrimental to the ability of the system to produce balanced, linear playback. Damping material and the use of low-resonance materials such as aluminium or wood in cabinet construction help prevent unwanted resonances.

Coda: Natural frequency, the hidden power of objects

  • When an object’s natural resonance frequency corresponds to the frequency of the energy applied to it, the object’s resonance frequency is amplified
  • Catastrophic resonance is the name for the unwanted destruction of an object due to an amplification of its natural resonance
  • When it comes to acoustics, great amplitude means higher volumes for the frequency in question – a physical fact that can work for or against a sound
  • In most cases, loudspeakers are designed to avoid triggering the natural resonances of any of their components
  • One example are bass reflext vents: Subwoofers with these types of construction make use of the Helmholtz resonance to enhance low frequencies

Title picture: By UW Digital Collections [No restrictions], via Wikimedia Commons

Natural frequency: The good, the bad and the catastrophic
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