Suppose a light wave with wavelength 3m. What happens if one tries to contain that wave within a 1m container? If I'm going about this entirely the wrong way or have wrong conceptions about light (which might be the case because I'm not a professional physicist), please tell me that instead.
Here is another hypothetical (i.e. extremely impracticable) answer to your question that is rather interesting (althgough Aksakal's Answer is likely to be a bit more practical!).
You have to imagine yourself to be a very deft light-catcher with mirrors (I can't help thinking here of Mozart the Light Catcher).
You trap light in the box by suddenly (within picoseconds!) putting your mirrors very deftly on nodes of the wave and so that their planes are aligned with the wavefronts. Then you squash the mirrors so that you end up with your light in the 1m long box.
What happens here is that the light will be blueshifted as you squash your mirrors together: it will be Doppler shifted by the moving mirror surface. So when you stop squashing, you can indeed prove that the nodes will still be at the mirrors and the light's frequency will have increased so that the nodes can be at the mirrors! Indeed, you can prove that the light's energy must increase (through the work you do squashing the mirrors together) by the same scale factor as the Doppler blueshifting factor. In other words, if you construe the light as being made up by a fixed number of photons, the photon energy must be proportional to the light's frequency. As such, this is a classical thought experiment that motivates the form (though not the constant $h$) of Planck's Law. See my answer here where I do the full calculation for "Squashing Light Into a Box".
Aksakal's answer is almost correct if you're talking about trying to contain light of a fixed frequency in a box smaller than the wavelength at that frequency. Otherwise put: modes of such a container are cut off at that frequency and are evanescent waves. So if you have a 100MHz source at the edge of a 1m square box, there will be a steady state field distribution in the box, but it will dwindle exponentially with distance from the source. Working out the full field in the box in this case is actually quite complicated: I believe it would be done in something like:
The light will die out quickly. Think of playing B tone on a string tuned to A. It's pretty much the same thing.
Also, 3m wave is not light, it's VHF used in TV
UPDATE: In the sound analogy, if you attach B tone generator to A-tuned string, as @WetSavannaAnimal suggested, there will be a B tone wave on a string, but it will be only at and around the point where the generator is attached. It will quickly die out along the string. The same is with your 3m wave generator, its wave will not full the box, it'll be localized around the source