There are multiple possible answers to this brain teaser, especially when one considers that a ring is simply a circular object with an empty center, or a generic term for a type of sound. For example, in the Solar System, the planets Jupiter, Saturn, Uranus and Neptune all have rings.
Also, older land line telephones equipped with an electric bell ring when the phone network indicates an incoming call. Thus, a phone is a possible answer to this riddle.
Lastly, people suffering from a condition known as tinnitus generally describe a “ringing in the ears,” although the condition can also be characterized by hissing, roaring, screeching and other disquieting sounds.