Long tones are at the core of most woodwind warmup routines. The most simple and obvious version is this:
Simple sustained notes are good for developing consistent breath support, which is required to keep the long tone steady in pitch, volume, and tone color. (Some teachers also suggest them for developing “embouchure strength,” one of the harmful and pervasive myths of woodwind playing.)
Many players and teachers recommend a version more like this:
But I like this even better:
The first thing to notice is the addition of extreme dynamic markings, from niente (“nothing,” essentially zero volume) to fff (which should be understood here as maximum controlled volume). Achieving a note that starts from 0%, crescendos smoothly and evenly to 100%, and then back to 0%, is much more specific and demanding than just a general “get louder, then softer.” It requires powerful breath support that starts before the note sounds and continues until after it ends, as well as a tuned-in voicing and well-functioning equipment. (And it can serve as a diagnostic to find issues in these areas.) Exercises like the David Weber chromatic exercises use this approach. (At the link, scroll down to “Longtone 1.”
Less-advanced players should start and end as softly as possible and work toward a true niente. Players at all levels should take the opportunity to discover and then improve their loudest dynamic level.
The second thing to notice is the addition of a tempo marking. This demands that the dynamic changes happen within a specific timeline, as of course they do in real-world music. Faster or slower tempos than the one marked here may be used; each presents its own challenges.
A very thorough long tone warmup might involve playing these on every note within the instrument’s range. Each will have slightly (or severely!) different demands. For a more practical approach, consider a rotation: on day one, do these on the instrument’s lowest note, and the note a fifth above that (or some other interval), a fifth above that, and so forth. The next day, start on the second-lowest note, and the next day the note above that, and so forth.