Arching or Raising the Tongue

A lot of teachers advocate raising the tongue to help with high notes.  The rationale is the Bernoulli principle, which you may remember from school.  Usually it is talked about it in terms of aircraft wings and lift, but there is another part to it that is relevant to us.  The idea is that when a fluid or a gas is traveling through a pipe and reaches a smaller pipe, the pressure increases in the smaller pipe:

_______________
                              \ _____________
lower pressure         higher pressure__
_______________/

Higher notes require more air pressure, and the theory is that raising the tongue takes advantage of the Bernoulli principle to help with high notes.  However, this is not the full story -- once the air passes the tongue and the air gets to the front of the mouth, the opening is bigger, so the pressure drops back down:

_______________                             ______________
                              \ _____________/
lower pressure         higher pressure__  lower pressure
_______________/                           \______________

I learned this from Arnold Jacobs, the great brass teacher and tuba player.  Whatever advantage you get from raising the tongue disappears, but now you have introduced the possibility of blocking the air with the tongue, which is what I used to do.  Instead of raising the tongue, just blow faster -- the more air molecules you put into the mouthpiece, the more the pressure increases.  Thinking of high notes as farther away from you can really help.  The higher the note is, the farther away it is.