Ask an Expert: Cymatics and Harmony Project

[SpencerO]

I am exploring the effects of musical harmony on liquids and powdered solids place on a membrane. What functions, equations, and algorithms will I likely need in order to understand the workings of cymatics?

[barretttomlinson]

Hi,

Here is a link to the a Wikipedia article on Cymatics:

http://en.wikipedia.org/wiki/Cymatics

And here is a link to a demonstration of visualizing patterns on vibrating plates:

http://www.physics.ucla.edu/demoweb/dem ... plate.html

I think you want to study sound, resonance, standing waves and nodes as the visualization techniques of cyma tics show you the node patterns of standing waves (salt particles accumulate at the nodes, where the plate does not move). A good place to start getting background is this Science Buddies experiment writeup:

http://www.sciencebuddies.org/science-f ... p012.shtml

Onxw you Hve read the page above the following links can help fill in the details:

http://www.physicsclassroom.com/Class/waves/

http://www.physicsclassroom.com/Class/waves/

To go beyond resources check out the bibliography links in Science Buddies writeup above or do searches using your favorite web search tool for the terms you need to know more about.

This project should be fun! Have fun with it.

Best regards,

Barrett L Tomlinson

[SpencerO]

Also, how do I go about using the Bessel Function to find the modes on a surface?

[barretttomlinson]

Hi,

How can you use Bessel functions to solve for the vibration of membranes? In my experience this question is usually addressed in second year college calculus classes. I am unclear on your math skill level, but doubt you are at this level. The short answer is to apply boundary conditions and find solutions which satisfy them. The boundary conditions for a circular membrane (like a drum head) are that the edge (rim) of the membrane is fixed(cannot move), which means the derivatives of position versus time at the membrane edges are 0. Here is a paper which discusses it further:

http://www.waset.org/journals/waset/v41/v41-57.pdf

And a Google book exerpt addressing the problem:

http://books.google.com/books?id=tbvuoA ... es&f=false

Here are some dynamic illustrations of several vibration modes:

http://paws.kettering.edu/~drussell/Dem ... ircle.html

You can find further discussion and derivations in many college calculus textbooks, including these:

Calculus, by Tom M. Apostol, volumes 1 and 2, BLAISDELL PUBLISHING COMPANY

Mathematics of Physics and Modern Engineering, by I. S. Sokolnikoff and R. M. Redheffer, McGRAW-HILL Book Company

Other experts on this forum, who have studied this area more recently than I have, have recommended other texts as being easier to use. You might ask your calculus instructor for recommendations.

I regret I cannot give you a simpler to understand answer.

Best regards,

Barrett L Tomlinson

[SpencerO]

Thank you, this information was extremely helpful.