indeed,
and the baffle also acts like a wind spoiler on a car streamlining the air going over it thus when no baffle there is a wider stream of air going through the mouthpiece, insert the baffle and the air stream is funneled and quicker and more powerful thus creating more projection too.
This is something I see often which I don't get
I think of sounds as standing waves. Frequency dictates pitch and amplitude dictates volume
Why should the forward movement of air have any influence on volume or projection? I can see that you might produce more volume if more air passes by the reed but is the forward movement of air through the mouthpiece really a mechanism that affects the amplitude of a standing wave?
I don't think very loud speakers 'blow' air any more than quiet ones
Even if the air in the mouthpiece was traveling forward fast enough to get the sound to your audience more quickly (and that's be something in excess of the speed of sound) surely the very nature of the cone shaped sax is that this forward velocity (of turbulent air) would diminish very quickly as the bore opens up?
This isn't me contradicting but trying to understand