Chladni Plates: Simulation vs. Reality

Inspiration

We were inspired by demonstrations of this effect shown on Youtube. We wanted to see if we could build a simulator to arrive at the same results and to build our own Chladni plate from scratch. This initial inspiration was incubated by Dawson's SPACE extracurricular program who sponsored our presence at the hackathon and gave us all the opportunities we needed to succeed.

What it does

In the physical model, we use an online tone generator to send sine wave sound frequencies to a speaker through a guitar amp. The speaker is attached to a driving rod, which acts as the vibration source for a metal plate attached to it. The vibration produces standing waves on the plate. By sprinkling salt on the plate we can visualize the nodal lines on the plate, as the salt will displace towards those line, away from the parts of the plate that are moving. The simulation displays a graph that represents a possible pattern of a square Chladni plate. Using interactive sliders you can change parameters to change the shape of the pattern to see other possibilities.

How we built it

We modded a guitar amp, replacing the built-in speaker with a speaker with a plastic cap, which allowed us to attach the driving rod to the center of the speaker. The driving rod is attached to the plate at the center. In order to keep the rod upright, we built a wooden support base which is mounted to the speaker. The simulation uses a given formula for representing the nodal lines of a Chladni plate derived from the 2D wave equation. Using a plotting library in Python we graphed the equation, displaying the Chladni pattern for the given parameters.

Challenges we ran into

Building the physical Chladni plate came with a host of challenges. Given our lack of construction resources, cutting the materials down to size and drilling the necessary holes took a good deal of time. Also, the patterns produced on the physical Chladni plate are very different from the complex patterns produced in the simulation, due to the nature of the build and the limitations of the materials. Plotting the equation ended up being more difficult than expected, as the library we used does not have an easy way of representing implicit curves (like the equation we are using). Another big challenge was getting the interactivity to work properly. However, we were able to eventually get over these challenges and arrived at the final product.

Accomplishments that we're proud of

The proudest accomplishment is that we actually managed to get both the physical and simulated demos to work in some degree. The challenges we had to deal with took a considerable amount of time and research to work through, as we are all happy that we arrived at a finished product we can be proud of.

What we learned

We had two major takeaways from this project. First, the math and physics of Chladni plates is much more complicated than any of us expected, involving 4th-degree PDEs and eigenfunctions, both of which are way above our level of knowledge as cegep students. Second, it is very difficult to build real simulations of physical phenomena in a way that closely fits the theoretical predictions. There are so many variables to take into account in the real world that being able to create a theoretically consistent simulation is a very difficult and impressive feat.

What's next for Chladni Plates: Simulation vs. Reality

With some more research, we hope to be able to find the relationship between the driving frequency and the patterns produced by the plate so that the simulation can be adapted to accept frequency inputs. Once we have a better understanding of the physics, we hope we can also simulate non-square plates, eventually arriving at simulations for arbitrary plate shapes. However, given that the math is complicated enough for square plates, we recognize that the second goal would require extensive research and significant dedication to complete.