|A table knife - preferably one that rings nicely if you hold the handle gently and hit it with something||Something to hit it with - eg. a pen|
Hold the knife at the base of the blade
Hit the knife gently - what does it sound like?
Hold it at the end of the blade - does it sound any different?
If you hold the knife at the end of the blade it will sound really dull and dead.
If you hold it somewhere near the top of the handle it will ring nicely.
Holding it at various places along the blade and the handle it will make other higher notes.
If you hold a knife by it's handle and hit the blade it can vibrate in various different ways. A vibrating knife will make the air vibrate which you will hear as sound.
|Not moving at all||The end just vibrating back and forth, this is the slowest vibration and called the fundamental.||The middle going right when the top goes left. This will be a higher frequency vibration (so higher pitch) and is called the first harmonic.||The bottom moving left while the middle moves left and the top right. This is even faster again and called the second harmonic.|
There are an infinite number of harmonics each one a higher pitch than the last. All of the harmonics apart from the fundamental have points where the knife isn't moving (nodes) and points where it is moving loads (antinodes).
|If you hold onto the knife at a node (where the knife isn't moving) the knife will not try to move your fingers so hardly any energy is used doing so and it will keep vibrating.||If you hold onto the knife anywhere else especially an antinode your fingers are going to get moved by the knife which transfers energy out of the vibration so it will quickly stop vibrating this way.|
When you hit the knife you make it vibrate in lots of different harmonics, which is why it sounds interesting. If you are holding onto the blade somewhere all the harmonics that are moving at that point die away leaving just those with a node there. So If you hold it in different places you will be left with different harmonics which have different pitches so it will sound different.
So why does it sound dead when you hold it at the end?
The one thing that all the harmonics and the fundamental have in common is that all of them move the end of the blade, so if you are holding there energy will get sapped out of all the harmonics very quickly and the knife won't vibrate at all.
Are harmonics important anywhere else?
They are the basis for music - if two notes have lots of similar harmonics that overlap, you will think they sound nice together, if they don't they will sound horrible. So the whole of music is to do with the physics of harmonics and vibrations.