It’s funny how you can use something so frequently and never consider how it works. I have played clarinet, off and on, for many years and I have not once thought about how my instrument actually works. But suddenly I was struck with wanting to know. I admit I was somewhat surprised when I typed in a simple google search for physics of clarinet and found a lot of results, many of which are posted on university sites.
The sound obviously starts with me. I blow air through the clarinet, but if I blow air the same way into space the only sound you hear is a slight wind. That’s where the reed comes in. The reed is a small piece of specially shaped wood that you attach to your mouth piece. How you set up your reed is important. It needs to be able to vibrate, tighten the ligature too tight and it becomes too hard to make it vibrate, and consequently make a sound. The vibration is what changes the sound of air into the sound of music.
To get a sound you need to have sound waves. This type of wave is a compression wave. The reed vibrates as I blow air past it, that vibration creates compression waves that create sound. I can change the note slightly by changing the pressure in my mouth and the position of my lip on the reed. But, that doesn’t explain how a clarinet can play so many different notes.
The clarinet has a huge range, much larger than most instruments. Each note relates to the length of the sound wave. The shorter the wave, the higher pitch the note will be. When everything is closed, which means you have covered all of the holes with your fingers and none of the keys are in use you can play a relatively low note, many lines below the treble clef staff. As you lift each finger up in succession the note raises in pitch by half a tone. What is happening is basically the equivalent of shortening the instrument. The sound wave is shorter and the pitch is higher.
If you are interested in reading more, or in looking at the physics of other instruments the University of New South Wales School of Physics has a lot of information and research about this, including a robot clarinet that they designed and built: UNSW School of Physics. Clarinet acoustics: an introduction.