Sound Meets Salt

It occurs to me that this kind of experiment is a nice example of showing patterns that occur without design.

I wanted to know where and how the sound was produced and how big the plate was.

The sound is coming from a speak right under the plate. I'm not sure how big/thick the plate is.

As the plate vibrates, the nodes of vibration are relatively static, while the internodal areas are highly dynamic, so that the powder -- salt, sand, or borax would do -- gets bounced off the dynamic parts and accumulates along the static parts. Changing the vibration frequency changes the positions of the nodes, resulting in a new pattern.

It matters that the plate is regular, otherwise no pretty patterns. Try this with a deliberately irregular edge and it would be interesting but a bit ugly.

The material also matters. The speed of sound through metal is much faster than, say, wood or cardboard, so the wavelength for a given frequency is much larger, making the nodes much farther apart and thus easier to see with the powder.

The salt is forming based on vibrations in shape of Lissajous figures - the wavelengths of the lissajous figures are changing depending on the speaker...

do i get a cookie? a crumb? a coal?

All I can tell you is it drove my dogs CRAZY!

6EQUJ5 is right. The sound waves are sinusoidal, and so they have peaks and "valleys." The salt falls into the valleys, and as the frequency changes, the position of the valleys changes.

I don't know if those are Lissajous figures (I don't know much about Lissajous figures), but I do know the precise patterns are caused by the interaction of the sound waves and the properties of the plate itself.

Resonant frequencies! Other people got to this before me so I won't say more. I'd give myself a cookie, but I ate my last one last night. I guess it's time to get more....

Indeed "cool", since I haven't seen the eigenmodes for a square membrane with free boundary before.

Nor I have seen anyone offer web cookies as a reward before. I'm a bit cautious with those. :-P

I don't know if those are Lissajous figures

Um, no. Lissajou curves are graphs of points following harmonic motions in 2 dimensions. That is what you can use on an oscilloscope if you want to compare phaseshifts of signals, before and after an electric circuit for example.

What you want is to find the solution for Laplace's equation for a square membrane with free boundary. Laplace's equation since it is a standing wave pattern.

I don't know offhand what it is called, but I think the figure of the corresponding solution for a solid sphere (Bessel functions) is illustrative.

The solutions to Laplace's equation, harmonic functions, have a lot of nice properties. They obey superposition, they obey a mean value principle (can't attain a maximum in the interior unless constant), and they are analytic ie locally given by a convergent power series.

The later connects to Fourier series, not surprisingly considering the wave nature of solutions. So the square membrane will have some Fourier decomposition, albeit you need a math software to handle it decently. FWIW, here is a description with figures I googled up.

When and if my comment on membranes comes up, I should clarify that Bessel functions are solutions to Laplace on the "spherical" membrane, and Legendre functions on the spherical solid...

Hmm... They are called "Standing waves".

The energy seems to be applied to the middle of the plate. The pattern is created by standing waves in the plate, caused by the reflections from the edges of the plates.

There are reflections because of the transition between mediums (i.e. plate and air).

The powder (salt) comes to rest in the zero energy areas of the plate, where the standing wave amplitude is close to zero, like 6EQUJ5 have said. The other areas have a higher energy hence create a less stable environment for the powder particles.

Another interesting phenomena is that not all frequencies create a pattern. Some frequencies (when the lines are sharp) don't create the right standing waves, i.e. there are no places on the plate with zero amplitude.

As the freq. generator is sweeping through the audio range, the lines start as fuzzy, then become very sharp for an instant, then become fuzzy again and blur. This is because in the beginning near one of those frequencies the wave going back and fourth "resists" the frequency difference by creating high frequency harmonics near the edges, and spot on the frequency they go away. If you listen closely you'll notice that some of the frequencies sound "clean" or "pure" sine, while other frequencies are sort of harmonized, the dmoinant frequency is less pronunced and there's some "fuzz". Or maybe it's the audio codec :-)

Also note how the higher frequencies tend to produce more of those standing waves, because it's easier to find a wavelength that would produce an even number of amplifying reflections.

-- Arik

Chladni patterns

Not only does the plate material affect the speed the sound waves travel through it, it also affects the frequency makeup of the waves emerging from the other side, which in turn obviously affects the patterns in the salt.

Half a cookie?

too cool indeed

Parts of the plate are hypertensive and have been warned off salt by their physicians. If KCl was used instead, no patterns.

So does the size and shape of the particles used have an effect? If it relies on how the particles jump around then that would be modified by the size and shpae, no?

Fascinating to watch!

My cat didn't like the higher pitches, either.

robin:

Hard to tell without observations and models.

But off hand I would think that the dynamics of the particles would be affected so that the formation time for patterns would vary. Heavier particles would move slower for the same energy.

You can get even neater results doing this to a non newtonian liquid. Click for youtube.