why salt/sand produces patterns when put on a vibrating surface,

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We all know the experiment right? putting fine grains on a flat surface and then pass a frequency through that surface. But why does it produce complex patterns? and why particular patterns at certain frequencies?

why do 2 dimensional sound waves manifest themselves as these complex shapes and patterns?

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In: 2

Because those specific frequencies produce things called “standing waves” where some parts of the surface are vibrating quickly, while at other parts, the vibrations cancel out completely. So the sand/salt gets bumped around, until it reaches one of those cancelation points (called nodes), where it stops.

And the specific orientation of nodes ends up being a pretty complex thing, where the material, thickness, and other properties all matter.

Any part of the surface that vibrates sends salt flying. After a short moment, the result is that all of the salt collects in places where it won’t go flying; places where the surface doesn’t move.

These places form when multiple sound waves collide, causing regions where they cancel out. This requires that they collide at just the right timing, and so it only happens in certain places and with certain frequencies that depend on the size and shape and speed of sound of the surface.

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If you stretch a string tight and pluck it, you see it moving up and down and make a noise. Depending on frequency, and string length, the string might vibrate in two places. The middle will looks like it is still. Translate that into two dimensions. The flat surface will have internal reflections from the edges, depending on the frequency of the vibrations. These reflections cause constructive and destructive interference, like dropping two rocks in a. pond. Some places the ripples will be higher, other places they will be flat.