In "ringing" a set of barrels you are basically
checking for loose ribs. If the barrels sound like a
"chime" with a mostly clear tone to each tube, then
chances are the ribs are well connected. If they sound
"dead" or "buzzy" then there's a chance the
ribs have come loose somewhere (or were never well laid to begin
with). It all takes practice and experience.
To do this afield:
1) remove the barrels from the gun and the forend.
2) suspend the barrels vertically a short distance over a safe
surface like a padded table.
3) use your left index finger in the "hook" of the
barrel lump to suspend the barrels (if you're right handed).
4) with your opposite index finger's nail,
"flick/tap/ting" one barrel along it's length. You can
also use a non-marring object like a pencil.
5) if the barrel "rings" then all is good.
6) repeat for the second barrel.
7) if the sound is dead or buzzy in spots, you might have a loose
But be aware that various barrels sound differently.
Composite barrels are more prone to have a bit duller ring to
them than fluid steel barrels. That is due to their construction
be of an iron and steel combination. Some are
perfectly fine, but don't chime well or much at all. Also... a
slightly loose/buzzy sound doesn't mean the gun is bad, it means
the rib might separate sometime in the future.