# standing waves

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We know what standing waves look like, on a string, or EM waves in a cavity.

But what's the mathematical definition of a standing wave? Does to have to include nodes, where the amplitude is always zero? And fixed end points? Can it be 2-D, or 3-D?

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Rich```
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Waves (as solutions to a wave equation) are standing waves when they have a recurring state (i.e. when they always return to a prior configuration). It's easy to do this with a box made of mirrors, and the mirrors are nodes in a sense, but it can also be done with other propogation-of-waves conditions. Standing-wave solutions are the resonances of bell, for instance.

A bell resonance is a three-D standing wave. The physical bell has some thermalization (the sound dies away), so it's not a perfect standing wave solution.

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** Standing waves on a drum skin are interesting:

And so is the math....

.... Phil

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a wave that fills a space with no energy being transferred by it

I would include ring lasers and surface waves on a droplet

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umop apisdn```
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or a liquid tin droplet.

```--
John Larkin         Highland Technology, Inc
picosecond timing   laser drivers and controllers ```
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Like this?

Amplitude of what? The particles of medium always are moving (but the directions are different). So the amplitudes never are zero. S*

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;)

Cheers

Phil Hobbs

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Dr Philip C D Hobbs
Principal Consultant ```
• posted

But that would include any oscillator, which doesn't sound right.

A bell is a 2-D surface, curved into a 3rd dimension, which leaves it still 2-D. Though of course it can support standing waves.

But still, it's an example, a picture. Given a ringing bell, what's the mathematical expression which defines 'standing wave'?

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Rich```
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Maybe this is too simplistic, but in one dimension a standing wave is really two waves of the same frequency going in opposite directions. It 2 dimensions it gets more complicated, but a similar idea.

George H.

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