Drums

Tony wanted a drum: A cajón. It’s basically a box with one wall thin enough to vibrate: The drumhead. The other walls are stiffer and / or heavier: One of them has an aperture. You sit on it to play. Inside can be empty, or it can have a snare-like mechanism.

Here you will find some details on how it was built, and what Tony put inside.

The geometry is the same as on stringed musical instruments with a cavity (e.g. the violin and guitar families), and can be analyzed as a system of coupled harmonic oscillators: Masses on springs with some damping. Because the geometry is fairly simple, we had a go at predicting what the lowest frequency would be, and how changing various parameters would affect that frequency.

Recognizing that we will regret this, we predict ~90 Hz and ~ 288 Hz for our design.

In our case the drumhead is made from Carbon fiber, and very stiff, as are the other walls. This means that, as built, we are really dealing with two almost independent oscillators, the Helmholtz resonance and the drumhead plate resonance, and they have very little interaction. The biggest challenge is then to estimate the end corrections for our particular wall-aperture geometry. Note the Helmholtz resonance is specifically defined as the frequency for an aperture in a rigid box. Our predictions for the uncoupled frequencies are: Helmholtz: 91 Hz, and Drumhead: 285 Hz.

Other materials are considered and show far higher coupling and very different frequencies can be achieved, even with the same geometry.