There are a few different families of musical instrument, each producing notes according to their own principles.
If you want to demonstrate the different families and the different principles in a classroom, examples of horns are perhaps the easiest to make. All you need is a section of pipe from the hardware store. I like PVC pipe the best, because it is cheap and lightweight, and is easy to find in a variety of sizes, but many pipes will work. Even mailing tubes or the cardboard tubes from paper towel rolls can work, although not as well as firmer material. If you can find them, bona-fide bull horns (such as the one below, which my father gave to me long ago), or ram horns (for example a shofar from a Jewish supply shop), or conch shells with the tip broken off, are all capable of projecting a very impressive bellow.
The trick with horns (or pipes, or shells) is to blow into them properly. If you played trumpet or tuba in your school band, you should have no problem with sounding a PVC pipe or a bull horn. If you haven't: You have to press your lips together as you exhale in just the right way to make your lips flutter as you blow. This takes a little practice, but it isn't difficult once you get the hang of it — some of us do it already when we want to make an especially exuberant sigh. How you form your lips will also depend a little on the size of the opening — smaller openings require a tighter pucker, and larger openings require a looser embouchure. If the opening is too tiny, making your lips flutter properly in the opening is impossible, which is why the bull horn pictured above has a trumpet mouthpiece stuck into the small end. It widens the opening.
With a tube the length of a paper towel tube or shorter, I have great difficulty making them sound, but I don't have much problem with any tube longer than that. With pipes around four feet long, I can even sound three or four different notes, like a bugle.Shell Trumpets, the Alpine Horn, the Didgeridoo, and all the instruments in the horn section of a modern orchestra, all work by the same principle. (There's a species of particularly large sea snail which was even given the name "Triton's Trumpet".) These are all essentially tubes, straight or coiled, used to capture and resonate the sound of a person's fluttering lips. If one wanted to give a scientific name to this family of acoustic tools that work on this common principle, the proper name would be labrophone. (Apparently Wikipedia and Google disagree with me on this, but I stand by my claim. Do any physicists out there want to chime in in the comments section?)
How Do You Make Different Notes?
If you have a few different diameters and lengths lying around, and maybe a metal pipe or two in addition to plastic ones, you may want to explore what makes the difference between different notes. Why does a pipe produce the notes that it does?
First of all, you will probably notice that you can play different notes by blowing differently — but only a few. You can't play just any note you want. There is one basic note, the lowest note you can play, and then as you tighten your lips, the sound will jump a few times to a higher note, before you reach your upper limit. This is what enables buglers to play (limited) melodies without having any moving parts on their instrument. We call the lowest note that a tube can emit the fundamental note, and the "ladder" of ascending notes we call a harmonic series. (If you listen carefully to the notes, you may notice that there does seem to be something curiously consonant or harmonious about those pitches. What's so special about these particular notes?) A talented bugler can normally play five or six notes of the harmonic series.
Second of all, if you are careful to compare only the fundamental notes of different pipes, you should be able to notice that the diameter of the pipe makes little or no difference, and the material of the pipe doesn't make much difference either. The only important factor controlling the (fundamental) note of a pipe is the length of the pipe. There is some vital property in the mechanical nature of a pipe that makes it produce the pitch that it does, and that property is length. Pitch goes with length. The diameter can make a difference in how easy it is to sound the pipe—This is the reason for mouthpieces. If the pipe is too wide or too narrow, you can't make your lips vibrate in the opening. The presence of a bell or a flare at the end can also make a difference—Brass instruments generally have a bell on the end because it makes them sound better, and this bell can affect the pitch. But if you stick with simple cylindrical pipes, as long as you can flutter your lips in the opening and produce the fundamental note, you should discover that all pipes of the same length will produce the same note. And the shorter the pipe, the higher the note.
This is how all brass instruments (other than bugles) make melodies: They produce a full scale of notes by having moving parts that change their length. The working of a slide trombone is obvious. You make the tube longer to produce a lower note, and make it shorter to produce a higher note. But how do you know exactly where to put the slide to produce exactly the right note? This is why most brass instruments have valves. They have a set of "detour tubes" of exact lengths, and when you press the valves, they divert your breath through one or more of these side-tunnels, making the total length of the tube shorter or longer by the right amount.
Now let's come back to the harmonic series for a moment. Why in the world would a single tube of a single length be able to produce a few different notes, and only those notes? What's so special about this harmonic series? Depending on the mathematical sophistication of your students, and depending on the pipes you have available, it might be interesting to see if you can explore this question...by comparing pipe lengths. Being able to relate audible pitch to measurable length gives us a way to compare notes numerically. So let's try an experiment: If we play, not the fundamental note of a pipe, but one note up, how much shorter would a second pipe have to be to play that same note, as the fundamental? In other words, if we had two pipes playing the same note, one as the fundamental and one as the first note up, how would their lengths compare? I never actually tried this as a classroom project, but in retrospect, it doesn't seem like it would be that hard to do. If nothing else, just try comparing two pipes, one twice as long as the first. You should discover that the lowest note from the shorter pipe is the same as the second note on the longer pipe. Or in other words, the first note in the harmonic series is somehow "twice" or "half" of the fundamental. It's more than I want to get into in this brief post on horns, but there's some very special relationship between the notes of a harmonic series, and simple integer ratios! A similar relationship is also the basis of the Pan Flute playing the Do-Re-Mi scale, or the Diatonic Scale.
Demonstrating that the Air is Vibrating
If you want to demonstrate in an unforgettable way that the air inside the horn is actually shaking, try dipping the end of a length of PVC pipe in soap-bubble solution. If you blow into the other end simply by exhaling, without sounding the pipe, you can blow a normal bubble at the other end. If you then repeat the demonstration, but this time flutter your lips and sound the horn, the bubble will provide you with quite a spectacle, and will illustrate quite plainly that there is a lot of vibrating going on—not just in the solid walls of the tube, but in the very air itself. It takes a little practice and a good thick soap-bubble solution, but it's worth it.
If you want to try this yourself, I can offer a few suggestions. You can buy bubble solution from Wal-Mart or many other home supply stores, but you can just as well make your own, from liquid detergent and water. I've been told by a science performer that Dawn and distilled water give the best results, in a ratio of about 1:10, and my experience agrees with that, although I prefer a bit more soap. Apparently, antibacterial agents or other additives to the detergent make the bubbles less durable, as does hard water. It is often suggested that you use a thickener, like corn syrup or glycerin, but I haven't found that it makes enough difference to be worth the trouble. (Every year at science fair time, I would suggest to students that someone do a research project to find the best bubble recipe, one that gives the most durable bubbles, but no one ever took me up on my suggestion.) Also, the end of a PVC pipe purchased from a hardware store can be a bit rough and raw, which is not good for bubbles. You may want to clean it and smooth it with sandpaper or steel wool.