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Writing on Standing Water
A reader writes "Engadget is reporting on Japanese scientists who have found a way to 'write' characters on the surface of water using waves. This looks very cool - but the time required to change character seems very high (15-30 seconds). From the article: 'Liquid-based displays are nothing new -- in a vertical orientation, at least -- but apparently it's a lot more difficult to coax a standing pool of water into forming recognizable shapes and characters.'"
Seems to be a popular pastime: http://www.theregister.co.uk/2006/05/31/huge_word/
That would be cool! However, it seems a little harder than this - in fact, it may not be possible.
If I understand the article (it's short on details) they're displaying an image by decomposing it into Bessel functions (like the Fourier decomposition in JPEG compression) and then having elements oscillate at different frequencies to recreate the shape. Bessel functions are the natural set of orthogonal functions for cylindrical symmetry - which is what the tank has.
The inverse problem is a little harder - determining the shape based on the observed frequencies. It's kind of like the problem of hearing the shape of a drum. It's possible for different shapes to have the same set of frequencies.
Sure, if you're willing to stick around for 6-12 minutes.