I had posted this under the "Free Blowing" topic, but Larry has asked if we could perhaps start a new thread for a different "take" on the issue: So here it is.
In my original post under the "Free Blowing" topic, I mentioned what I feel is the mechanism that makes a trumpet "free blowing". In response, several posts were made to the effect that the penultimate sound of a trumpet is more often appreciated by the audience and that you don't want to lose too much of that sound through the vibration of the horn itself. (I may have paraphrased a bit much with that last statement but I think you get my drift).
While I was writing my post I was thinking about a link that I'd seen on one of the "old" GR mouthpieces website. It had been replaced when their site was redesigned, but thanks to Brian Scriver, I have the link "back again". Personally, I was blown away when I first saw the research that had been done; I'd never thought of the WAY that a trumpet bell vibrates, nor thought through how that energy gets partially reflected back into the air column AS WELL AS radiating off of the outside of the bell. Further, I'd never really considered how it can "color" the sound of a trumpet. Dave's post really "turned on a light" for me when he mentioned the Thomas Moore article and connected "impedence" with "sound out front" rather than "horn design" (which is the more common link).
Here is the page which shows a trumpet bell being "excited" at different frequencies. Note the pattern of the "nodes" which are moving the greatest distance (and creating the greatest vibrations in the air...hence "sound production"). See how there are more nodes but they are "tighter together" with the higher frequencies and notice how they extend back "down" the bell flare towards the bell tube. Then imagine a horn with different bell material, bell thickness, thickness variance... think about the effect on the vibrating node PATTERN with bracing at a different spot along the bell tube/throat.
http://vanadium.rollins.edu/~tmoore/research2.htm
I had written an email to Professor Moore asking him about the apparent "discontinuity" at F=1194 and F=1356; he explained that there actually ARE more nodes at 1356 but that they extend down the bell and towards the rim a greater distance. (As far as I know, this is the same Dr. Moore who wrote the ITG article). The only thing I would absolutely LOVE to see is a video clip of the node pattern as the frequency is continuously increased; I'd like to watch the node pattern move back up the bell towards the bell tube and then "break up" and create a different pattern to support a greater number of vibrating "nodes" (or panels).
The dark area in between the lighter nodes are areas where the vibration is relatively low. Truly amazing stuff to think of a bell shape vibrating with this pattern...looks like a steel drum!
Enjoy the link....and thanks, Brian and GR.
Ed