Most people are familiar with wrinkling of skin at old age, but may not have thought about wrinkling beyond that. Wrinkling is actually a much more widely observed physical process: it is also responsible for the development of fingerprints at a young age, and the creasing of the skins of fruits that have been left out for too long. Luckily for us, the explanation for it is pretty interesting and like so many scientific phenomena, you don't need any technical know-how to get the gist of it.
To understand how wrinkling works, first imagine a thin sheet of a stiff material, such as a bank card. If you try and compress it along its length, then it would bend away from its original position.
From experience we know that it would always form this arch shape - approximately the shape of half a sinusoid (try this if you're not sure). If you try to force it you can also get the card to accomodate that compression by bending twice, forming the shape of a complete sinusoid.
This takes a lot more energy to do because you are effectively bending the film twice as much, and you can feel that trying to force the card into this shape is quite difficult. Extending this idea, you could imagine that it is possible to get the card to bend many many times in order to be compressed by the same amount as before, but that will take a lot of energy to achieve. In general, the card wants to form a single arch and bend as little as possible.
In fact, you'll probably break your bank card before you get there. On the other hand, imagine a thick piece of a soft elastic material, like a sponge. When you compress this, it would rather just squash up in the same direction that you are compressing in. No bending required.
So, the interesting stuff starts happening when you stick your thin stiff material on top of your thick soft material. So long as the two are properly attached, then when you start compressing you will have a mismatch in interests between the stiff sheet and the thick soft material - so what shape will the system prefer in this case?
In the leftmost scenario above, the thin stiff sheet is happy because it bends as little as it possibly can, meaning that it is in its lowest energy state. However, this shape requires that the soft elastic material must stretch itself by a large amount to fill the void left behind by the film. In the case on the right, the soft elastic material is much happier because there are no big voids to fill in - only several small ones. But this scenario isn't favourable to the stiff sheet material, which has to expend a lot of energy to bend into that shape.
So the result is a compromise. Bending only a few times to make very large waves is not allowed because the elastic material must be stretched by a large amount, whereas bending an infinite number of times to get infinitely small frequent waves is not allowed because the film would have to use an infinite amount of energy to bend into that shape. So, that means that you end up with wrinkling on the surface with a finite wavelength and amplitude.Why might you want to know this? Well, aside from it being fun to understand things, wrinkles can be used to change the way materials behave. In my research, a one of the things that I've tried to do is to make the wrinkles as small as possible. Once they get down to below one thousandth of a milimeter in period (wrinkle length), light starts behaving quite wierdly around the surface, changing direction based on its wavelength, and this behaviour is being exploited in research to improve the performance of future solar panels.