Good and Bad Resonance

If you push your friend on a swing once, your friend oscillates a few times and stops. This frequency where the swing oscillates on its own is called the natural frequency. If you give a push each time your friend swings back to you, your friend swings higher and higher. You push with a frequency that is the same as the natural frequency, and the amplitude of the oscillation grows. This behaviour is called resonance. Surely, this shows that resonance is a good thing. Actually, there are good resonances, and there are bad resonances.

Pushing the swing is an example of good resonance. Another one is heating food in a microwave oven. A third one is the antenna on a radio receiving the radio signal. A fourth is playing the flute. There are many more.

How about bad resonances? Shattering of a glass with a high pitch voice is one, unless you want the glass shattered. Breaking of a bridge by a gentle breeze is another. Collapsing of some buildings by earthquake is a third.

It is usually a bit tricky to understand how the ideas I have developed from pushing a friend on the swing can apply to the different examples above. Lets start with the antenna on the radio.

A radio has to receive the radio wave sent out by the radio station. By the time this wave reaches your radio, it is very, very weak. Somehow, the electronics in your radio must be able to sense this very weak signal, so it can amplify it into your news or music. This is the purpose of the antenna. The radio wave moves the electrons in the antenna, and the antenna can produce a current that is big enough to be felt by the electronics in the radio. How does it work?

A radio antenna is usually a long, thin metal rod or wire. Radio wave is an electromagnetic wave. It is made up of an electric field and a magnetic field that oscillates and can travel through air or vacuum. This means that when it reaches the antenna, an electron in the antenna would feel an electric force that keeps changing direction. This is the effect of the oscillating electric field. It moves the electron, together with many others, and produces a current along the antenna.

The electrons in the antenna has a natural frequency. When an electric field is on, the electrons would be pushed towards one end of the antenna. If the field is then switched off, the electrons would repel each other and push themselves towards the other end of the antenna. When the repelling forces get to big at the other end, the electrons would move back again. In this way, the current oscillates at the natural frequency. This frequency depends on the length of the antenna. The trick is to choose the antenna length to give a natural frequency that is equal to the frequency of the radio wave. Resonance is then possible. The very tiny force from the radio wave would push the electrons at their natural frequency in the antenna. The current would grow until it is big enough to be detected by the electronics. This is the good resonance in the radio antenna.

Lets look at an example of a bad resonance now. Many years ago, there was a bridge called the Tacoma bridge. Ever since it was built, it had swayed gently in the wind. This bridge had a certain natural frequency. The bridge carries a road with cars and trucks driving past.

One day, the wind just so happened to blow at a frequency that was roughly equal to the natural frequency of the bridge. The bridge started oscillating with a larger and larger amplitude. Luckily, all the cars and trucks had time to drive off the bridge. The bridge heaved up and down and bent at unnatural angles. It got stretched and distorted more and more until it cracked and collapsed.

This was a bad resonance. After this experience, bridges were built to avoid such a resonance. This could either be to use much stronger support so that the natural frequency is higher than could be reached by the wind. Or friction may somehow be added to damp (reduce the amplitude of) the oscillation.

(Well, maybe not all bridges. There is a wooden, suspension foot bridge across the Bridgewater Canal at Walton Hall in Cheshire, near where I live. This is a favourite place for children. Each time I walk along this bridge, I can feel myself oscillating up and down a few times per second. What would happen if a group of children step across this bridge at exactly the same frequency?)




Copyright 2010 by Kai Hock. All rights reserved.
Last updated: 15 May 2011.