Ring true

What is the meaning of "ring true"? Thanks.

I'm pretty sure this relates to church bells. A well cast bell will sound the correct note - it will 'ring true'. If there's a defect in the bell, then the intended note will be false. By ananolgy those things which 'ring true' are considered correct.

"Ring true" is in fact the motto of a college that I know. What does it mean in this context then? How would you define/explain the word "ring" here? Thanks.

I would assume this was calling upon the students/alumni to strive for excellence and not exhibit any faults - figuratively speaking, to be like that perfect bell which "rings true," leaving a good, inspiring impression on their "audience"... ?