Here's how to glue a crack shut so it'll be stronger than the surrounding wood.
My African folding chair
I fixed it with epoxy thickened with wood dust. That's usually the best thing, but use whatever you've got. Even Elmer's school glue is okay if the crack isn't separated too far.
If you're fixing a valuable musical instrument talk to a luthier about glues. They'll suck you into a glue-filled time-vortex.