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🎵 This time, I decided to create something you can hear as well as see.
✨ Open The Drum That Splits a Note
Imagine a perfectly square drum. It has two entirely different patterns of vibration that produce exactly the same pitch.
Now stretch the square ever so slightly.
The two pitches separate.
I made an interactive sound experiment where you can strike the membrane, watch its vibrations, change its shape, and listen to what happens.
My favorite experiment is to choose “Tiny stretch”, then strike the drum off-center. The two frequencies differ by only about 2.7 Hz, producing an audible pulsing phenomenon called beating.
There's also a little mathematical mystery: both of these particular vibrations disappear when you strike the drum exactly at its center. Why?
The experiment includes the explanation, an interference graph, and the exact eigenfunctions and eigenvalues of the rectangular membrane.
I tested the controls and calculations in a browser. It works offline, including on mobile, with synthesized sound.
What I wanted to capture is a rather beautiful idea: symmetry can force two completely different things to have exactly the same value. Breaking that symmetry reveals a distinction that was there all along. 🌿
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