Drummers drum simply because that’s what drummers do. If they weren’t drumming, they would no longer be called drummers. If a plumber stops plumbing and begins drumming, I would say at that moment, he is a drummer. Now, if that plumber was locked inside a sound-proof room with no doors or windows, with a drum, then at any given point he may or may not be drumming. There’s no way to know. Thus, you can only assume that he is both a drummer and not a drummer at all times, simultaneously. That is the little known (i.e. fictional) Schrodinger’s Plumber Experiment.
Erwin Schrodinger, more known for his theoretical work with cats, was a Nobel-winning physicist. Richard Feynman was also a Nobel-winning physicist. Professor Feynman loved drumming. Thus, all mathematicians love drumming. QED.
Actually, since the 195os, mathematicians have been wondering whether it’s possible to hear the shape of a drum. The sound of something is determined by the frequency of its vibrations, which is then flavoured by the timbre of overtones and harmonics. With research papers bearing exciting titles such as “Can you hear the fractal dimension of a drum?”, or “The Riemann zeta-function and the one-dimensional Weyl-Berry conjecture for fractal drums” some very smart people have spent a lot of time on the question. Those smart people have more-or-less concluded that no, the eigenvalues of bi-axisymmetric manifolds cannot… er… no… a unique shape does not guarantee a unique sound.
So let’s talk round drums. Most drums are round, outside of theoretical cat-torturing land. It’s a membrane, stretched across one end of a hard round frame. Technically it’s called a membranophone, which we learned when we were learning about the origin of the kazoo. The acoustic properties of a drum are actually more complex than a guitar, despite being a much simpler instrument. A guitar string is one-dimensional (length) and so the vibrations are pretty simple. A drum head is two-dimensional (length and width) which leads to many more ways for it to vibrate and interfere with itself.
The smaller the drum, the tighter the skin, the faster the vibrations, the higher the pitch. A single-ply plastic drum head gives a bright springy sound, while rock stars prefer the flatter thud of a multi-ply skins. The body of the drum is also built to shape the sound as desired. Like blowing across the lip of a bottle, a large drum holds more air having a deeper resonance. A thicker wall will absorb more high-frequency waves, letting a lower frequency sound eminate.
There’s a lot of physics going on here. So clearly, if you want to grow up to be a rock star… stay in school, kids!
And thus, we conclude the Twelve Facts of Christmas. Hope you have a happy Twelfth Night celebration, and that you whoop it up Shakespearean style!