Tuesday, April 17, 2007


Quick review:
Frequency: number of oscillations per second.
Period: time taken for one oscillation.
Amplitude: maximum displacement from equilibrium position (rest position) of the particle or pendulum.

We've all heard urban legends of people being able to break glass, or more usually crystal by singing at high pitches. Some of you would probably also have seen this picture:

This is the famous Tacoma Narrows Bridge just before its collapse, which started tilting left and right on a particularly windy day. If you can find the video clips detailing the collapse, it's quite amazing.

All of these phenomena, and much more, can be attributed to the natural phenomenon of resonance. So what exactly is resonance?

Every object, when excited in some way, vibrates at a very special frequency known as its natural frequency. For example, in the lab experiment you just did with the pendulum, the pendulum has a natural frequency that can be calculated. Those of you who still haven't handed up you lab report, you can verify that this formula is true:

Where T is the period of the pendulum, pi is just pi, l is the length of the pendulum, and g is the acceleration due to gravity, which is 10 m/s^2.

So a pendulum when set into motion will automatically start moving at this period or frequency called its natural frequency: the frequency at which it oscillates when it is not disturbed by anything. Anything that is able to oscillate has a natural frequency, a kind of preferred frequency at which they like to oscillate.

This also happens when you blow air across a half-filled bottle to produce a sound: this sound has a certain frequency that is the natural frequency of the air inside the half-filled bottle. When you let your arms swing naturally by your sides, they should be swinging near the natural frequency. When you hit a drum, or a string, or when you produce a note on a wind instrument, you are making the skin, string or air vibrate at its natural frequency.

But of course, in a pendulum, I can try to force it to oscillate at a faster or slower frequency by trying to control the motion with my hand: I can grab the string above the pendulum bob and try to make it go faster or slower by moving my hand faster or slower than the natural frequency.

You can try this at home with a broom stick. Grab the top of the broom stick with one hand, and allow it to swing naturally, without you exerting any force. It will start oscillating at its natural frequency. Now, you can try to make it swing faster by applying a force through your hand. Observe what happens to the amplitude of the swing as you try to make it go faster. You should see the amplitude getting smaller and smaller, and the broom swinging less and less.

If you try to make it oscillate really really fast, by moving your hand back and forth really really quickly, you would actually see the broom not moving at all! This is because it has no time to react to your motion before the direction of motion suddenly changes, so it'll just sit there and watch you.

Now let it swing freely again, and then try to oscillate it really really slowly with your hand, and compare the amplitudes when it's swinging naturally, and when you are trying to oscillate it really really slowly. You'll probably notice a slight difference: when you try to interfere with the oscillation, sometimes you are going against the natural movement of the broom, and hence you are slowing it down and decreasing the amplitude.

It all sounds pretty confusing, but when you try it, it's quite apparent.

Now try to move your hand back and forth at the same frequency at which it is naturally swinging. I'm sure you'll see the difference: the amplitude of the swings will increase greatly, because your force is always going with the direction of motion, so you are making the oscillations greater.

So this is the lesson we learn: if we try to oscillate anything at its natural frequency, it will produce an oscillation with very large amplitude, that will increase with time if you continue to make it oscillate. This phenomenon, where you try to make something oscillate at its natural frequency to produce really big oscillations is known as resonance.

So here's how we break glass with our voices: we tap the glass to hear the sound it produces: this sound is the natural frequency of the glass. We then match our voices to that natural frequency (we just have to match the pitch of the note: what we hear as pitch is actually the differences in frequency) and try to oscillate the glass molecules at its natural frequency. Due to the phenomenon of resonance, the glass molecules will develop very high amplitude oscillations. If these waves are large enough to break the bonds between molecules (just like they were strong enough to break the bridge apart in my opening picture) then the glass will shatter!

I don't think it's easy to do, but at least it is possible in theory.


Altaris said...

the concrete and steel looked like paper!
zhu chong

Altaris said...