For these explorations, you should have two pieces of spaghetti—one short, and one long—both with marshmallows on top.
To begin, hold the free end of the long piece of spaghetti in your hand. Using your other hand, gently pull the marshmallow a centimeter toward you and release. Observe the vibrations, and try to get a sense of how rapidly the marshmallow vibrates back and forth. The number of times something vibrates back and forth in a period of time is called its frequency, and when an object is allowed to vibrate on its own accord, that’s called its natural frequency.
Dampen the vibrations of the spaghetti with your free hand. Now start shaking the long spaghetti again by moving your hand only a small distance back and forth, starting with only a few shakes per second (a low frequency). You are making the spaghetti to vibrate at the same frequency as your hand. Making an object vibrate is called a forced vibration.
Slowly increase the number of shakes per second, and force the spaghetti to vibrate at a higher frequency. The marshmallow will probably twitch but its motion will remain relatively small at first. As your hand’s frequency goes up, though, at some point the spaghetti will suddenly start to vibrate a much greater distance back and forth, even though your hand is only moving a small distance back and forth. When an object is forced to vibrate at the same frequency as its natural frequency, it’s called resonance.
When an object is in resonance, a series of small vibrations can add up to create a larger vibration. Look at how much your hand is moving compared to how much the marshmallow is moving. Your hand is barely moving, but the marshmallow is moving a lot. Can you vibrate the marshmallow enough so that the spaghetti breaks with only a small motion of your hand?
Repeat the above steps with the shorter spaghetti. Does the shorter spaghetti-and-marshmallow arrangement have the same natural frequency as the longer one? Do you have to vibrate your hand at the same frequency to make resonance occur or do you need to shake your hand with a higher frequency?
Try the two spaghetti sticks at the same time. Hold both in one hand so that they make a “V”. Start shaking your hand. Can you get both marshmallows to move a large distance at the same time? That is, can you get both pieces of spaghetti to be in resonance at the same time?