1) Take a length of pipe and hit one of the open edges with the palm of your hand.
2) Attach an oil funnel to the same pipe and hit the edge of the pipe that doesn’t have the funnel with the palm of your hand.
3) Do you notice any difference between the sound of the pipe being struck when it has a funnel attached to one and and when it does not?
4) Try the same experiment but instead of hitting the pipe with your hand, try using a mouthpiece to blow through the instrument. Do you notice a difference with and without the bell?
The bell acts as a resonator.
According to wikipedia, “A resonator is a device or system that exhibits resonance or resonant behavior, that is, it naturally oscillates at some frequencies, called its resonant frequencies”. The bell’s resonator properties will make the instrument sound louder.
But they also effect the frequency at which the instrument will resonate. They raise the pitch of the lowest natural resonances of the instrument. This makes the whole instrument work better as a unit and makes tuning the instrument easier.
Try a couple of different shapes of funnel. Do you hear certain funnels working better with certain lengths of pipe?