I need to know this because I need some information about ringing tones for a science project that I am doing. I have tried researching, but I could not find any information.
A ringing tone on a string instrument (not just violin) happens when the instrument is perfectly in tune, and the player plays a note (also perfectly in tune) which causes a sympathetic vibration in an open string.
For example, with the violin, a very straightforward ringing tone is when the D string is not touched and the player plays a "d" on the a string. The d being played is an octave above the open d string, but if played exactly in tune, the open d string will start to vibrate "in sympathy".
If you listen very carefully for such ringing tones when beginning to learn the violin, they can be a great help in the process of playing properly in tune.
Actually, my insistence above, that the note must be perfectly in tune is not totally true: you will get a ringing tone if you play a note which is very slightly out of tune with an open string, but you will certainly get a louder ringing tone (which will also ring longer after you stop playing the note) if you are precisely in tune.