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?
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.
** Standing waves on a drum skin are interesting:
And so is the math....
.... Phil
a wave that fills a space with no energy being transferred by it
I would include ring lasers and surface waves on a droplet
or a liquid tin droplet.
"RichD" napisal w wiadomosci news: snipped-for-privacy@googlegroups.com...
Like this?
Amplitude of what? The particles of medium always are moving (but the directions are different). So the amplitudes never are zero. S*
;)
Cheers
Phil Hobbs
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'?
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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