talking about xylophones
In: 4
Think of a ruler. If you fix it at one end and apply a force at the top, it will move the top pretty far. It has a low stiffness due to being so long and slender. Now cut the ruler to only 2 inches and apply that same force to the top now. It only bends a little bit because it is much shorter. This short piece has a much higher stiffness because it is much shorter.
When we talk about vibrations, we are really talking about what the natural frequency of the piece of material. The frequency will increase with stiffness and will decrease if you add mass. Since we know shorter objects are stiffer, this makes the pitch higher for the short object.
I can get into more detail if you would like, but I wanted to keep it relatively simple for ELI5.
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