Discovering Drum Head Patterns for Music Education

[Curiousgeorge77]

Hey everyone - I run a music school and learning about how sound works is really helpful in talking about tone production, volume, and just understanding in general what's going on. As part of that,. I'm looking for a pattern that I could print on a drum head that would show how the head moves. My first though is the resonant head of a bass drum (not the side that is struck, but the one facing the audience) although the side of a snare drum that the drummer hits would be even better.

Any thoughts/suggestions? Thanks!

 

[berkeman]

Welcome to PF.

Printed patterns on a drum head won't help you unless you use a strobe light to watch them. Do you have access to a strobe light? Otherwise, you could use sand or other small particles to watch the resonances on the drum head.

 

[anorlunda]

There are many vibration modes to a drum head.

 

[Curiousgeorge77]

Yeha - and they all happen at the same time, but the 1st+4th are the most clear. However, if you put that image on a bass drum it isn't immediately obvious what's happening.

How can I make it so that anyone will see the movement without an explanation? (not necessary understand the physics, see the modes, etc, but see the movement)

 

[Curiousgeorge77]

You can see the way they move here in slow motion

 

[hutchphd]

The problem is that each of the normal modes oscillates at a different frequency and these are not commensurate in a simple way for a drumhead. So one can either individually excite them with a pure tone from a speaker or isolate them with a strobe light at frequency. Otherwise the motion will be a mish-mash I fear.

But I do have a good word: cymatics. The stuff with liquid surfaces and light is wonderful.

 

[Wizard]

You might be able to use the drum as a Chladni plate, by attaching a speaker to the bottom side and playing sine waves through it. See here:
https://sciencedemonstrations.fas.harvard.edu/presentations/chladni-plates
I'm not sure how well this would work for a drum in practice but the principle is there. I have difficulty seeing how else you would be able to demonstrate the vibrational modes of the drum.

I'm not sure what your physics background is so here's the gist. The drum will have a number of resonant frequencies $\omega_i$, each of which is associated with one or more of the oscillation 'modes' which are pictured in the image shown by anorlunda. Here's an interactive demonstration of what the oscillations modes like:
https://demonstrations.wolfram.com/NormalModesOfACircularDrumHead/
Fortunately in the case of a drum it's a very concrete demonstration. The plot is showing the skin of the drum, displaced up or down, although this displacement is greatly exaggerated compared to a real drum. An arbitrary vibration of a drum skin is modeled as a linear combination of these vibrational patterns.

If you play a tone through the speaker at the bottom of a chladni plate (or a drum) at a frequency that matches one or more of the oscillation modes, $\omega_i$, then the drum will naturally vibrate in response with some linear combination of all the modes that have that specific frequency. You can see in the linked demonstration that the vibrational modes are indexed by $n$ and $k$. If you take care to vibrate the drum right at its center, then (hopefully) all the modes with $n\neq 0$ will not be stimulated. Only the modes with rotational symmetry, like the first and fourth modes in the image shown by anorlunda.

Each of the modes with $n = 0$ has different frequencies, so it should be possible to stimulate one at a time. This is what you want, because then you can see the parts of the drum skin that 'nodes' which remain fixed and do not oscillate up and down. If you just hit the drum, you would get a linear combination of modes and no particular points on the drum skin would be stationary except the outer rim. When you cause the drum to oscillate in a single mode, particles on the drum (e.g. fine sand, maybe styrofoam?) will take something of a random walk on the drum due to the agitation back and forth as the drum skin flaps up and down. However those particles that randomly make it to one of the still spots in the drum skin will stay there undisturbed. This may also be due to static friction which keeps particles hugging the skin until the skin 'falls' underneath them, causing them to actively seek out nodal points. I'm not sure.

In any case, the point is that if you put a speaker under the drum right at the center, place fine sand on the drum with good contrast, and scan through a range of sine wave frequencies, you ought to be able to observe this effect of the sand collecting in the nodal points of the oscillatory mode. You could demonstrate the different vibrational modes by scanning through the frequencies finding the higher-frequency modes.

 

[Curiousgeorge77]

It'll be chaotic, yeah - but you'll be able to see the 1st and second harmonic motion if tuned properly and struck exactly in the middle before it devolves.

Cymatics is GREAT! Have you seen this video? I'll use to show the kiddos to explain what's going on. I'll get feedback from parents about how the kiddos talk about science at the dinner table lol :)