Wednesday, May 5, 2010

What a vibrating reed looks like

I've long wondered what exactly reeds look like in motion, and how exactly does the various scrapes affect their behavior. If you look at the reed-making literature and traditions, there are many views, most of which share little in common. You'd think the study of acoustics ought to be able to help, and maybe it can, or has for some, but I haven't figured out how yet.

One clue may come from a classic undergraduate physics demo, the Chladni pattern. The coffee cup image shows a kind of Chladni pattern, formed by shaking at 20 Hz. I've found similar patterns by dragging a filled styrofoam cup across a smooth surface, setting up a slip-stick motion.

Classically, Chladni patterns are formed by putting sand on a thin plate (say, a violin top or back) and vibrating it, by . The sand collects along lines where the plate isn't moving, which is to say the nodal lines of the mode. These patterns are actually useful to violin makers, who can assess the symmetry of their carving, and adjust the frequency of the modes by examining these. The lines separate regions which are moving up from ones which are moving down. The pic here is taken from the great acoustics site at UNSW, and corresponds to mode 7 of the violin back.

If sand on node lines is too low tech, well, you can always play with lasers. Picart and friends made some kind of fancy laser interferometry/digital holography contraption, which allows the visualization of not just the nodal lines, but also the full 3d deformation of the vibrating structure, time resolved if desired. They applied this to a clarinet reed, with the images seen here. They've also used these to study all kinds of things about clarinet reed motion, which might be very interesting if I could manage to decode their paper. One thing is clear, though. The clarinet is the best studied reed instrument, among other reasons because the reed's natural vibration frequency is very high, which reduces interactions between the reed's resonances and the air column's. The very lowest frequency in the pictures is 1880 Hz, which is about a Bb6, essentially out of the usable range of the clarinet. So yeah, even for the highest notes on the clarinet, the reed should just flap open and closed, without getting all contorted.

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