A quick test for a good violin or cello
i use the tap test first and tap the top and back of the instrument with a finger(or if you have long fingernail use the knuckle instead.
a high note means the wood is heavy and hard for the strings to resonate the instrument.
the second test i use a tuner that tells me what the note of the string is(believe it i am tone deaf )
i detune the bottom(base) string and listen to the note .
at some time the sound will change from a boing to a sort of flapping sound.
this point is where the weight of the string is no longer able to move the violin/cello and if you feel the instrument while it is being plucked you will also detect the note below which the instrument loses it resonating ability.
the lower the note the better the instrument generally.
set up and other things will determine other playability qualities.
in most of my instruments the g string of my violins can still resonate at 7 notes lower-- ie g below the g
on most cheaply made violins you are lucky to get 3 notes below befor it stops shaking.