Lesson 47: Standing Waves and Resonance

In the last section you saw how waves can build each other up or rip each other down (by constructive or destructive interference).

There are a couple of things we can put together to see an interesting effect based on this.

• If you are pushing a little child on a swing, how do you make them go higher?
• Well, you make sure that you time your pushes so that you push in sync with the way they are already swinging.
• If you push randomly or out of sync, then the child will never go very high.
• This is an example of constructive interference causing the simple harmonic motion of the child to increase. We give this kind of "in sync" motion the special name "resonance."

## Resonance

To understand the special type of constructive interference mentioned above, think of the following (and slightly more scientific) example.

• You tie off a piece of rope to the wall, and then stretch it out.
• Standing at the far end you flick your wrist to send a wave pulse to the other end.
• When the pulse hits the wall, most of it will be reflected back towards you as an inverted wave.
• If you hold the rope tightly with your hand, the wave would hit your hand and most would be reflected away from you as an erect pulse… but instead, you flick your wrist again at exactly the instant that the first wave hits your hand.
• The two waves are now both traveling away from you, both erect, and both on top of each other. Their amplitudes will add together to make a bigger wave!
• Keep doing this over and over again and the wave keeps getting bigger.

In the above example you are making sure that the frequency of your wrist flicks matches the frequency of the wave itself. This is resonance.

• In any of these examples, the frequency of the wave itself is equal to the frequency of new waves being created. We would say that the new waves are being created at the “resonant frequency.
• You might have heard of someone singing to break a wine glass. It is recorded as having been done once, and the singer didn’t have to sing loud. She just sang at the resonant frequency of the glass.

According to legend, a large number of Roman legionnaires were moving from one location to another by foot. They had to cross a rather large bridge to get across a large river. As they crossed the bridge, they continued to walk as every good soldier is trained to… in sync. Left, right, left, right, etc. You can imagine that this started some waves shaking through the bridge. Unfortunately for the legionnaires, they were walking in just the right (or I guess from their view, wrong) way that the waves they were creating with their marching were adding onto each other constructively. The amplitude of the waves increased rapidly until the bridge finally collapsed under their feet! Most of them died from the fall or drowned in the water. How's that for a resonant frequency!

Do a search on the internet for the "Tacoma Narrows Bridge" to see an extreme example of modern day resonant frequency. This bridge fell apart because the winds blowing across it matched its natural resonant frequency. You can watch a brief video of "Galloping Gerdy" (as the bridge was called) bouncing around by clicking here. You can also view pictures in my Picture Gallery.

## Standing Waves

Standing waves are just an extension of the concept of resonance.

• Suppose you now made sure the wavelength of the wave you made in the rope example above was exactly double the length of rope.
• You would get something that would look like waves bouncing through each other.
• Now double the frequency, and you get even more waves bouncing through each other.
• In each of these examples you are creating a wave that just seems to be sitting there bouncing up and down.
• We call these standing waves since they don't look like they are actually moving back and forth like regular waves, just like they are standing there bouncing up and down.
• Any part of the wave that never moves is called a node, while any part that has maximum amplitude is called an antinode.

Watch a video of me making standing waves (with a giant spring!) by clicking here. Requires Windows Media Player 9 or later and a broadband connection (dial-up connection not recommended).