The lip end behaves acoustically like a closed end of an aircolumn
(pressure antinode), while the bell end behaves like an open end
(pressure node).
The tubes behave like a closed tube with the fundamental having
a wavelength approximately four times the length of the tube.
The size and shape of the mouthpiece affects predominantly
frequencies of the upper resonances.
The bell has two important effects:
It provides the proper coupling or impedance `match' between the
instrument and the outside air to transfer the sound most efficiently,
making the sound considerably louder.
It modifies the frequencies and stability of the resonances,
especially the lower ones.