What follows are some notes I wrote for Jordan Hoffman during a recent FB PM exchange. I did some edits for the blog and I put them in italics, to be clear.
Jordan, I’ll do a blog about this later, so I’ll use Word to write you some notes on your question.
OK, in an extreme nutshell here is how a trumpet works.
The lips are the vibrator that inputs acoustic energy in the horn. You close your lips up and then begin to increase the pressure in the oral cavity by blowing. When the pressure is high enough it blows the lips open inject a puff of air – a pulse – into the wind column, which is the horn. The pulse travels at the speed of sound (340 m/s at STP). It reflects off the bell barrier – an “inertial barrier” in the vicinity of the bell of the horn. I’ll circle back to that later. (I never did circle back in the original exchange, so I will here!)
Due to the nature of the free end reflection the phase of the pulse is reversed (if we focus on air pressure rather than molecular displacement). It was injected as a high pressure or overpressure pulse, but upon reflection it is inverted and comes back as an under pressure pulse. It travels back towards the lips at the speed of sound and arrives at the lips as an under pressure. Now the magnitude of the under pressure pulse is reduced somewhat because it dumped some acoustic energy into the room (the sound we hear).
Now, if you just pop the horn with your hand the sound dissipates very quickly. In order to keep it going we have to help the rapidly dwindling pulse wave rattling back and forth in the horn. However, if we “let” the lips open up at this point and dump a high-pressure pulse into the low coming back to the lips we’ll just kill the wave. We have to wait. The lips will remain closed. The low-pressure pulse will reflect off of the closed lips, but here is the tricky part. The pulse isn’t inverted at the closed lips, so it leaves the closed lips as a low pressure and goes back to the bell barrier. Then it reflects again but it inverted into a still weaker high-pressure pulse which comes back to the lips. NOW we let another high pressure pulse dump into the weaker high pressure pulse coming back to the lips and instead of canceling, we have supported (reinforced) the wave and help sustain a build up of acoustic energy with a leaky system. All of the reflection of the bell barrier leak some sound into the room, but that is what we want.
Now, hopefully it won’t be too much of a stretch that the distance from the lips to the bell barrier and the constant speed of sound means that this process only works with the timing at certain frequencies, the notes that come out of the horn.
That is an ultra simple and concrete explanation. I hope it makes sense.
Next, When you hit those specific notes where the reflections and outgoing pulses all cooperate to keep the energy building up in the horn you are dealing with a process called resonance. Any time you have outgoing waves mixing with reflected waves, you can achieve resonance at very specific frequencies (notes). Another name for all of this is regenerative feedback. When you hear feedback in a PA system, you are getting the same phenomenon playing out. The amplification of the sound is from the waves continuing to pile up on each other and you keep pouring energy into the system by blowing harder.
If you check out my vids you’ll find one where I break a wine glass by blowing my horn. You can see this process of energy build up there. When I take a breath I hit the note again as quickly as possible before the glass has a chance to stop vibrating. By doing this I can make the energy build up as a standing wave in the wine glass till the motion is too much for it to take.
You ask about the motion of the molecules. This can get a little weird when it comes to explain the bell barrier. Let’s skip that for now. I will remind you the there are TWO components of mole cure motion in the wind column. There is the back and forth motion of the sound waves. Then there is the drift of the air we have to blow between our lips to make them vibrate. This of the back and forth motion as the AC part (because the electrical analog is totally accurate) and the drift as the DC part. In fact the DC part doesn’t have to even go through the horn at all to make it work. I have a mouthpiece into which I drilled a hole into the die into the bowl. I take a trumpet and tape mylar over the bell so no air can get through the horn. Then I put the special mouthpiece into the horn and put straws of specific lengths to vent the mouthpiece out of the side instead of through the horn. You can play the horn just fine, though with a muted sound. There is no DC through the horn. I didn’t dream this one up. There is an ITG article from some years back where this was done with a trombone.
I did promise to circle back to the bell barrier. How a sound wave reflects off of an open bell is a little more than I want to try to deal with here. Suffice to say that I referred to it as an “inertial barrier” earlier. More advanced physical acoustics uses flange theory to deal with the reflections. It can be addressed more concretely just by discussing inertia, but I can milk another blog out of that! ;-) Here is one more piece. The reflection points in from the bell barrier actually MOVE! The lower the note the further back in the bell they reflect! As you approach a high G the reflection point is right at the end of the bell flare. As you ply higher the horn doesn’t resonate well, so not slots beyond, say, a high A.
Now ALL high note players that there are very distinct slots for DHC. This is quite true, and it is acoustically counter intuitive. I even demonstrated this when my physics teach group did a presentation at the American Acoustical Society convention in Chicago some years back. I challenged them to explain the noticeable resonance slot for DHC that should be there. They were all stumped! Hah! I got a kick out of that. I have a theory and I alluded to that last week in the gap blog. I will work up a demo and make a vid for a discussion later on.
Finally, Jordan, check out these vids and see if you can track them with these notes.
Note that the second one is simply edited or truncated. I’m just dumping in in here in case I missed something.
Here is one on breathing, but the bubble demo addresses the concept of drift or DC part and the sound or AC part, tacitly. The DC part is very low and barely moves the bubble. The bubble is flexible and the sound travels right through it.
OK, here are some bonus vids, because I hate to be forgotten as a musician when I go after all of the physics stuff.
Jordan, you’ve inspired me. I’m going to do a series of blogs/vlogs about all of this.
Finally, if you’re interested the best book on the subject is this:
The Benade book is more famous, but the explanations Backus offers are much more concrete.
I hope this all helps. Feel free to reach out anytime you have questions on this stuff. I t just be easier to call me.