I guess I can weigh in on this one, as an organ-builder in residence - maybe there are others, too?
According to correspondence I've had with a handful of whistle makers in the past Michael Copeland being one of them, some whistle makers have studied, in various ways, organ pipes and applied their observations with whistle construction - as is mentioned in the interview with Mr. Copeland that DrPhill noted.
The terminology is a bit different – blade or ramp = upper lip, block = languid, etc., but other than that, a whistle is a the same as an organ pipe, it just has to make play more than one pitch - which in my career voicing pipes makes it quite mysterious indeed. I've no need to try it - at least efforts that would be made public!
Anyway, the 'walls' are called ears on an organ pipe, and much like if you hold your hands in that position on either side of your mouth and sing or make a sustained tone, you can hear a focusing, of sorts, of the sound - as you would do when you are calling for someone. Ears aren't a requirement, but really a matter of tonal preference of the voicer or tonal designer of the instrument. They do become a requirement when they hold a "beard" or "bridge" of some sort, of which there are many types and for various purposes.
The type of beard that Copeland uses is commonly called a box beard. Its most common use - and again there are always exceptions - is on organ pipes that are capped or closed at the top - commonly called Quintaton or Quintadena. Normally, the upper lip (blade) of a capped pipe is cut-up high enough to make a flutey sound, which is what capping the pipes does, harmonically. However on the pipes that use a box beard, the cut-up is lower than usual, and the pipe wants to overblow to the next harmonic. Positioning a box beard - for whatever reason based in physics - allows the pipe to speak, not overblow to the second (octave) harmonic completely, and helps emphasize the 3rd harmonic, which is an octave and a fifth - hence the name quintaton. They are very fussy beasts to voice, believe me!
If I had to guess at what the box beard is doing on a whistle, I would say that it is in order to get a strong bell note - I have a Copeland silver C here with ears and a beard. That would allow whistle maker to make the whistle a little "quicker", that is the languid or block is a bit lower (or the upper lip is rolled out a bit more) which allows the top notes to speak more easily, but the result is that the lower notes also want to overblow easily. So, the ears and beard are there to keep the whistle from overblowing on the bottom end, and the effects of the ears and beard aren't nearly so prominent in the top end - likely to the point of not really affecting the speech.
DrPhill, as for proportions of the ears and beard - there are no cut and dried rules. Box beards can be added after the ears as a separate piece that bridges the ears, it may or may not contact or conform to the lower lip, and it (and the ears) may be wide or narrow. Over the years I've worked with pipes from European and domestic builders and supply houses and everyone has their own set of proportions. I would say to experiment and do what works, but don't get too caught up in what may or may not be ideal. If it works for you, then there you are!
Did that make any sense? There's certainly a wealth of information on the web about this, though some of it I've read obviously wasn't authored by a voicer, so it tends not to make much sense, or is perhaps too theoretical to be practical. As any instrument maker knows, and if there's one thing I've learned after voicing thousands of pipes, there are always exceptions to the rules.
If I'm ever working in anyone's area, you are more than welcome to drop by and I'll be glad to give a lesson or two! If you can get your hands on some metal organ pipes, you will see quickly - and I will be delighted to assist - what I mean. That said, my hat is off to the whistle maker for taking what I would call a single-note pipe and working his magic and poking it full of holes so that it becomes a whistle!
“Fear is the path to the dark side.
Fear leads to anger. Anger leads to hate.
Hate leads to suffering.” - Yoda