Chladni Figures I

XR_XharpRazor

2 days ago

2 min read

What it is ?

A speed run to understand Chladni Figures

Take a rope, fix it at one end, then shake the other end once,

a pulse is sent to the end, and bounce back.

If you continuing shaking the rope at a correct frequency

the pulses you sent and the pulses that bounces back

will add up to become a new wave :

some parts of the rope moves, some part of the rope stays (aka "nodes").

This wave is what we call "Standing Wave"

The same idea applies for a Metal plate.

Fix the metal plate one a pole, put some sand/salt on it, and vibrate it.

If a grain of sand is on a part of the metal plate that moves a lot, it will keep bouncing around

until it "finds" a place where the metal plate does not move that much

(aka the node)

How it works ?

Prepare to get flushed by LATEX

let's say for now, we found a shape that a metal plate can wiggle,and we freeze time. we can then describe the metal plate as :

we call the cyan part the "Shape Function".If we now consider to let time flow, we will oscilate the shapelike so :

usually by convention, the cyan part is ranged between -1 to 1.sometime we might wiggle the metal plate way further or way subtle.This means we need to scale it with an Amplitude :

On a Rope, let's say you found a frequency that the rope has a single buldge.

This frequency is what we call a "Fundamental Frequency", for short, let's call it "fund"

On a string, there are other frequencies that cause the rope to go into "Standing Wave mode", usually "2fund", "3fund", "4fund" ... "Nfund"

these are all the ways that a rope can wiggle in "Standing Wave Mode"

The same thing happens on a metal plate :

different frequencies can excite different modes ("shape").

if we were to only focus on one shape, it should look like this :

but since a metal can vibrate in multiple modes,and sometimes a frequency can excite multiple Modes, we will have the following :

Seeing what we are hearing

time to put sand on the plate

The main idea of KOwOdni is like what we do on the metal plate :using the sand to draw patternssince the sand lands on the part of the metal plate where it barely moves, we can have :

let's say at a very specific moment, say t = T, sin(ft+p) reaches it's biggest magnitude, but there are parts of the metal plate not vibrating. this means :