I'm doing a research on recorder, and I got a little stuck on the part of ranges. Some says the soprano recorder's highest note goes to the 2nd octave only, but some people say that by adding a recorder bell the pitch can be higher. What exactly is a recorder bell and how do you add one to the recorder, thanks!
It's not a bell, it's a bell key. The bell is just another word for the end of the recorder (where most of the air comes out), and a bell key is a small construction that can partly cover the bell up.
The recorder can be made to play higher by carefully covering the bell -- sometimes people do this with their upper leg, but from my own experience I can tell you that it's quite difficult to pitch correctly this way. A bell key is easier to use (or so I hear -- I have never tried it myself).
The bell key described by Lee White was invented by Dr. Carl Dolmetsch (special keys )to help the fingering for the very difficult high C#/F# (soprano/alto) note, one half-step below the the high D/G (2 octaves+1 whole step) that all baroque or modern-design recorders should be able to play easily. Without the key one must indeed stop the bell (close the bottom of the recorder) with your knee or a pillow or something similar. Some professionals can do this with ease, even playing fast notes. It's quite showy when done well.
Composers like Telemann, Handel, etc., knew this very well and very rarely called for that note.
There are fingerings for notes above that top D/G but each recorder is different and so they won't all work and most are usually very difficult to use in practice. Telemann's highest note for alto recorders is C7, which can be played cleanly but not quietly on quality instruments.
What's happening now is that modern recorders are being made longer and have an extra key or two to provide better hole spacing for the lowest holes and even extend the range down a half-step or more. This results in better, simple fingerings for the ultra-high range, so a bell key isn't needed for those instruments. See the Mollenhauer website for an example: Soprano with B Foot
The highest note on a recorder depends on the type of recorder.
The highest regular note on a baroque (default) instrument is the whole tone above the second octave, e.g. the third D on a soprano in C (which I have in fact played in concert).
The highest regular note on a Ganassi-fingered (i.e. renaissance reproduction, conical-bore) instrument is the fourth above the second octave, e.g. the third F on a soprano in C. (Fingering chart here.) It does not require bell covering. (I ♥ my Ganassi.)