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Define coupled and uncoupled please. My guess is that coupled means a back joined to sides which are 'coupled' to a top joined to the sides as well. (i.e. a closed box)

But...

Well, coupled as used here is in an acoustic sense, but that only applies when the box is closed, so you were not far off.

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The name catgut is confusing. There are two explanations for the mix up.

Catgut is an abbreviation of the word cattle gut. Gut strings are made from sheep or goat intestines, in the past even from horse, mule or donkey intestines.

Otherwise it could be from the word kitgut or kitstring. Kit meant fiddle, not kitten.

The linkage between any two items, causing one in some way to follow the other. The way that the second follows the first can often be described with mathematical precision thus defining how the two items move in relation to each other. The term is used in physics and engineering to describe the interaction of two or more oscillatory systems. Effective coupling is evident if the frequency of the oscillators in the coupled system is significantly different from the frequency of the oscillators when they are uncoupled. When effective coupling occurs between two systems, the frequency difference between the resonant systems increases (i.e. the resonances can be said to repel each other)

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Trevor Gore, Luthier. Australian hand made acoustic guitars, classical guitars; custom guitar design and build; guitar design instruction.

http://www.goreguitars.com.au

What Trevor said..

One point of all this is that once you glue the box up there are lots of ways for the different parts to push against each other, and influence the way the other parts work. When Fred made up his electric circuit model of the guitar he could specify the values of the elements that modeled each part in isolation. Thus he had an inductor, a capacitor, and a resistor that modeled the 'main back' resonance and another set of electrical components for the top. It's relatively easy to calculate the resonant pitches of the electrical circuits in isolation. With a guitar, you can't do that. The resonant modes that the top and back show when they're off the guitar don't relate very simply to the modes of the assembled box, and once you've glued things together they're 'coupled' acoustically in a number of ways, so you can't really talk about 'the' back or top resonance by itself. That's why there's some disagreement about the 'best' way to measure these things.

In practice, this stuff an get complicated. 'Way back when I made a little guitar for my daughter to learn on. It had a small body and a short neck, and when I stuck the back on with sticky tape the 'main top', 'main air', 'main back' and 'neck' resonant modes were all within a semitone of each other as far as I could tell. I wanted to drop the 'back' mode a bit, and tried to shave the back braces to do that, but no matter how much material I took off them everything stayed where it was. I finally realized that this was an example of the sort of 'pushing' that Trevor talks about: each part was shoving at the others like kids in line in the second grade. They worked out an arrangement where each of them was 'comfortable', and no amount of exhortation by the teacher could shift them. In the event, it turned out to be a wonderful little instrument, but she didn't play it for very long. Playing the guitar was much harder than daddy made it look...