Understanding cymatics physics

[bartsam]

TL;DR Summary

Relationship between sound frequencies, cymatics plates size density and sand patterns/shapes

Cymatics devices using sand allow us to create shapes with sound. Do you know if those shapes depend on the density and the size of the plate? Thank you

 

[robphy]

Possibly useful:
https://blogs.scientificamerican.com/but-seriously/chladni-figures-amazing-resonance-experiment/
https://skullsinthestars.com/2013/05/02/physics-demonstrations-chladni-patterns/

 

[Baluncore]

Welcome to PF.
The plate vibrates in different modes, at different frequencies.
The sand shows the nulls in the standing wave pattern, that are set up in the plate when the sound frequency is a multiple of the fundamental resonant frequency of the plate.

 

[nasu]

The frequencies of the modes depend on the density, shape and size of the plates. And the stiffness too.

 

[bartsam]

Welcome to PF.
The plate vibrates in different modes, at different frequencies.
The sand shows the nulls in the standing wave pattern, that are set up in the plate when the sound frequency is a multiple of the fundamental resonant frequency of the plate.

Thank you Baluncore!

I'm not sure you're answering my question or maybe I'm not formulating it correctly…

 

[bartsam]

The frequencies of the modes depend on the density, shape and size of the plates. And the stiffness too.

I'm not sure what "(frequencies of) modes" means…
Does it mean that with the same vibration produced by the device, the plate would have different frequencies depending on the density shape and size of the plate? Therefore different sand shapes?

 

[nasu]

The resonant frequencies will be different. The shapes may or not be different. You see the shapes when the frequency of the vibrating device is close to one of the resonant frequencies of the plate. You may see the same shape (or similar) on different plates, but at different frequencies. The shape depends on the geometry too. The modes of rectangular plates have difefrent geometries than for circular plates.
For a given plate, there is a set of vibration modes, each one corresponding to a specific frequency. This set of frequencies depends on the geometry and physical properties of the plate.

 

[Swamp Thing]

You may find this interesting and helpful.

 

[berkeman]

I'm not sure what "(frequencies of) modes" means…
Does it mean that with the same vibration produced by the device, the plate would have different frequencies depending on the density shape and size of the plate? Therefore different sand shapes?

The resonant frequencies of the mechanical plate will depend on the driving frequency(ies) and the dimensions of the plate. Usually the resonant frequencies will be harmonics of the driving frequency. The amplitudes of the resonances in the plate will depend on the stiffness and thickness of the plate, and the patterns will depend on the size and shape of the plate (the "boundary conditions").

Can you say a bit more about your background in waves and resonances in basic physics? That will help us to tune our responses to hopefully help you best. For example, do you understand how the linear density of a string and the tension in a string help determine the resonant frequencies in a stretched string (like a guitar string)?

 

[nasu]

The resonant frequencies are specific to the plates and do not depend on the frequency of the driver. They are the frequencies corresponding to the normal modes of vibrations.
The plate vibrates with the frequency of the driver, as any forced oscillation. As you change the frequency of the driver, anytime the frequency of the driver is close to one of the normal modes frequencies, the amplitude of the plate vibration is increased, as for any resonant system. The frequencies of the normal modes for plates are not harmonics (not integer multiples of a fundamental frequency).
The frequencies of the normal modes depend, besides the parameters of the plate and the geometry, on the boundary conditions of the plate. Which side(s) are free, which are clamped, etc. will result in different normal modes.

 

[bartsam]

The resonant frequencies are specific to the plates and do not depend on the frequency of the driver. They are the frequencies corresponding to the normal modes of vibrations.
The plate vibrates with the frequency of the driver, as any forced oscillation. As you change the frequency of the driver, anytime the frequency of the driver is close to one of the normal modes frequencies, the amplitude of the plate vibration is increased, as for any resonant system. The frequencies of the normal modes for plates are not harmonics (not integer multiples of a fundamental frequency).
The frequencies of the normal modes depend, besides the parameters of the plate and the geometry, on the boundary conditions of the plate. Which side(s) are free, which are clamped, etc. will result in different normal modes.

ok so the shapes are dependent on the plate itself not this or that frequency; the driver and the sand only reveal the (resonant frequencies or) the intrinsic physical nature of the plate…?
Thank you very much for your explanations

 

[bartsam]

The resonant frequencies of the mechanical plate will depend on the driving frequency(ies) and the dimensions of the plate. Usually the resonant frequencies will be harmonics of the driving frequency. The amplitudes of the resonances in the plate will depend on the stiffness and thickness of the plate, and the patterns will depend on the size and shape of the plate (the "boundary conditions").

Can you say a bit more about your background in waves and resonances in basic physics? That will help us to tune our responses to hopefully help you best. For example, do you understand how the linear density of a string and the tension in a string help determine the resonant frequencies in a stretched string (like a guitar string)?

I don't know much about waves and resonances physics… I'm curious and understand more or less the notion of harmonics in sound and objects/matter. Thank you!

 

[Baluncore]

ok so the shapes are dependent on the plate itself not this or that frequency; the driver and the sand only reveal the (resonant frequencies or) the intrinsic physical nature of the plate…?

To excite the plate, you must find a mode of vibration and a driving frequency. Only then will you see a pattern.
A bow from a stringed instrument can be used to quickly excite a plate at its resonant frequency, without needing to search for a particular driving frequency, because the edge of the plate can be "plucked" by the stick-slip drag of the resin covered bow string.

 

[nasu]

ok so the shapes are dependent on the plate itself not this or that frequency; the driver and the sand only reveal the (resonant frequencies or) the intrinsic physical nature of the plate…?
Thank you very much for your explanations

Yes, the plate and the boundary conditions. You can easily find the vibration modes calculated for plates with free edge, clamped edge or "simply supported". By "easily find" I mean in books or papers. To calculate them is quite a job.
They have different patterns and different frequencies even though some modes may look similar. Now I have my book handy and I looked up some formulas. For a circular plate with free edge the frequency of the lowest mode is given by $f_{20}=0.2413 \frac{c h}{a^2}$ where c is the speed of longitudinal waves in the plate, h is the thickness and a is the radius. The speed of sound depends on the material's density and stiffness (Young modulus for longitudinal waves). So these are all the parameters that determine the frequencies.
The next higher frequency is 1.73$f_{20}$, the third one 2.328$f_{20}$.

 

[robphy]

Possibly useful:





https://thelig.ht/chladni/

https://www.desmos.com/calculator/vmp1kbn9ml

• You can modify the rate of the slider animation (e.g. to slow it down) using the Properties button below each play button.
• Zoom in to a region to see a more fluid animation.
• variant: https://www.desmos.com/calculator/rcwjdw5i1o