Resonance

Resonance

Have you pushed someone on a swing before? You have to stand behind the person on the swing. Each time the swing comes back to you, you push as it is going forward again. You only need to push with a small force each time. After pushing many times, the swing swings higher and higher. You energy has accumulated in the swing!

What I have just described is an example of resonance. Resonance happens when a force pushes or pulls at an body repeatedly, causing the amplitude of oscillating body to grow. A force that is used to help with the oscillation is called a driving force. Not any force can cause the amplitude to grow. The force has to act in certain ways. The above example contains some hints as to what these are:

You have to push each time your friend swings back at you. This means that your force must have the same frequency as the swing.
The frequency refers to the frequency if your friend swings on his own, which is what happens when he swings back at you. This frequency is called the natural frequency.
You have to push only when the swing swings forward to get the biggest effect. If you push when the swing is still on its way back, you would just slow it down. This means that your force must be in phase with the oscillation.
What if you push at a different frequency from the natural frequency of the swing? If you do so, you would find yourself pushing sometimes when the swing comes towards you, sometimes when it moves away from you. At times you help it to move faster, at times you slow it down. On the whole, your driving force is not very effective. So the amplitude does not grow much.

There are many examples of resonance. Sometimes they are good, sometimes they are bad.

You may have heard stories or seen videos on how a wine glass shatters when when a lady sings at a very high pitched voice. This can really happen. Think of a glass on a table. Take a spoon and gently hit the glass. "Chink ..." You hear a high pitched sound. The glass vibrates for a short while. It is not actually moving left and right when it vibrates. The glass may compress and expand repeatedly, or the oscillation may be more complex. The wall of the glass is actually getting distorted in some way. Normally, the ampitude is too small to see with our eyes alone, but is enough to cause the air to vibrate and produce a sound. The frequency of this sound is then the natural frequency of the glass.

Suppose a lady standing next to the table is able to sing at the same pitch. Her voice causes the air around the glass to vibrate. The air molecules push at the glass repeatedly, from all around the glass, in a complicated way. It is a very small force, and can only cause a very small oscillation in the wall of the glass. However, because the frequency of the force is the same as the natural frequency, the air molecules that happen to be moving in the same direction as (i.e in phase) with the oscillating glass wall will increase the amplitude of this oscillation. After many oscillations, the amplitude, and therefore the distortion, of the glass wall, grows. If the lady keeps up her singing, the distortion can become so large that the glass breaks.

So that was an example of bad resonance - unless you want the glass to shatter. What is an example of good resonance?

One such example is the microwave oven. The way it works is that the microwave causes the water molecules to oscillate. By giving energy to the molecules in this way, the food heats up. Each molecule in water is surrounded by other molecules. It can move, but not very freely. If you push a molecule, the neighbouring molecules coud push it back. In this way, the molecule can oscillate a bit. The natural frequency of this oscillation is about 2 GHz - i.e. two billion times per second. But how can you push a water molecule?

It turns out that the water molecule is polarised. This means that it has a very small electrical charge on one side, and the opposite charge on the opposite side. This happens because the oxygen atom in the molecule attracts electrons more strongly than the hydrogen atoms. An electric field can cause these electrical charges to move, and drag the molecule along. Microwave is actually a combination of electric and magnet fields that keeps changing direction at a very high frequency. We call this an electromagnetic wave. When microwave goes into food, the oscillating electric field applies a force repeatedly on the water molecule. If the frequency of the microwave is at 2 GHz, then this force is at the same freqeuncy as the natural frequency of the water molecules. The oscillation of the molecules grows. In effect, they take energy from the microwave. The energy in this motion is just the internal energy. In this way, the food heats up.

The Physics Notes