I... Did I know this_

I... Did I know this?
Tim HuttonTim Hutton - 2014-01-06 22:42:39+0000 - Updated: 2014-01-06 22:45:21+0000
I... Did I know this?
Shared with: Public, John Baez
John Baez - 2014-01-06 23:04:31+0000
If you make little waves in your bathtub or sink and let them bounce off the wall, you can get this to happen.
Tim Hutton - 2014-01-06 23:05:59+0000
+John Baez : stay there, I'm going to fill the sink...
Tim Hutton - 2014-01-06 23:35:44+0000 - Updated: 2014-01-06 23:40:07+0000
+John Baez : Yes, pretty much: (video: [John Baez told me to make standing waves in a sink]) I put a plastic bowl in the sink and bounced it with my hand and there was definitely a resonant frequency. But I don't quite see the connection between the moving solutions to the wave equation and the standing wave solutions, other than the image above.
John Baez - 2014-01-06 23:51:47+0000 - Updated: 2014-01-06 23:54:26+0000
I haven't looked at your video (though I love the title).  But the idea is that one wave moves from your hand to the edge of the sink, while its reflection moves from the edge of the sink back to your hand, and if you time things right they add up to a standing wave.

In a nutshell,

sin(t-x) + sin(t+x) = 2 sin(t) cos(x)

At left we have a sum of two waves moving in opposite directions; at right we have a single standing wave.

It can be easier to see if you have a long bathtub, and you wiggle your hand sending a pulse of short-wavelength waves to the end, and watch what happens as it bounces back and crosses over itself.  It's not always so neat as the image above, but you can get standing waves.
John Baez - 2014-01-07 00:19:24+0000
I looked at your video.  The wavelength of the waves is so large compared to the size of the sink that it's sort of hard to see what's going on.  A large body of water, with short-wavelength waves, makes it easier.  Sometime I see this phenomenon very naturally when a gust of wind over a swimming pool sends some ripples to the edge and then they bounce back, forming standing waves as they overlap themselves.
Tim Hutton - 2014-01-07 00:49:00+0000
I've been learning (in a casual way) about the wave equation and the Schrödinger equation. Is it true to say that the standing waves in the Schrödinger equation are the reason we have quanta of light and electron orbitals and so on, or is that a different phenomenon?
Tim Hutton - 2014-02-24 13:25:31+0000

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