What is the concept of Physics of Cymatics (of a liquid)

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Discussion Overview

The discussion centers on the physics of Cymatics, particularly the patterns formed on liquids when subjected to varying frequencies or amplitudes. Participants explore the underlying concepts, potential formulas, and mathematical approaches related to these phenomena.

Discussion Character

  • Exploratory
  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • Some participants inquire about the physics concepts behind Cymatics and whether there are specific formulas that describe the patterns formed in liquids.
  • Others explain that Cymatics makes the modes of resonance visible, likening it to sand on a vibrating metal plate.
  • There is a suggestion that simpler patterns can be described by equations based on the surface shape, suspension method, and driving frequencies, while more complex patterns may require simulations and could involve complicated mathematical solutions.
  • One participant mentions that Boundary Value methods are used to solve these problems, referencing the 2D wave equation and the concept of standing waves, particularly in the context of a drum head.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the physics of Cymatics, with some agreeing on the visibility of resonance modes while others seek clarity on the existence of specific formulas or patterns. The discussion does not reach a consensus on the complexity of the mathematical solutions involved.

Contextual Notes

Limitations include the potential complexity of mathematical solutions for Cymatics patterns and the dependence on specific conditions such as boundary shapes and suspension methods, which are not fully resolved in the discussion.

Rosella Lin
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Hi,

Could someone please help me about what is the physics concept behind Cymatics. Is there a formula which establishes the patterns form on a liquid when the frequency or amplitude are changed?

Thanks.
 
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Rosella Lin said:
Hi,

Could someone please help me about what is the physics concept behind Cymatics. Is there a formula which establishes the patterns form on a liquid when the frequency or amplitude are changed?

Thanks.
Are you familiar with the basics of waves and resonances? The wikipedia article is a good starting point:

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

:smile:
 
Yes I have studied waves and resonances but I don't understand what is going on with the patterns of the cymatics
 
Rosella Lin said:
Yes I have studied waves and resonances but I don't understand what is going on with the patterns of the cymatics
It's just a way to make the modes of resonance visible. Like when you put sand on a vibrating metal plate...
 
ok i see. But is there no formula or pattern it follows?
 
Rosella Lin said:
ok i see. But is there no formula or pattern it follows?
For the simpler patterns, you can generally write the equations that show what the pattern will be, given the shape of the surface, how it is suspended/held, and the driven locations and frequencies. For the more complex patterns, you could probably simulate them, but if there are good mathematical solutions, they are likely to be complicated (like, beyond what I can try to help you with).

Nice web page with tutorials and cool videos/pictures -- http://doorofperception.com/2013/11/cymatics/

:smile:

http://www.dustino.co/nnor/wp-content/uploads/2014/11/cymaticsgold.jpg
cymaticsgold.jpg
 
Mathematically, these problems are solved using Boundary Value methods:

https://math.dartmouth.edu/archive/m23f09/public_html/drum.pdf

and here:

https://en.wikipedia.org/wiki/Boundary_value_problem

Basically you define how the edges of the boundary, use the 2D wave equation and through the magic of partial differential equations come up with a family of functions that solve it.

As an example, a drum head has a non-moving circular boundary and so it limits the kinds of waves known as standing waves that can occur:

https://en.wikipedia.org/wiki/Vibrations_of_a_circular_membrane

From there you can determine nodal lines ie where the head doesn't move and that's where the sand on the drum surface will tend to sit.
 
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