To Sound
To Ring
intransitive verb, godan verb
You learned 鳴く means "to chirp" (or some other animal sound). 鳴る is similar, but it's used when something just makes a sound, like a phone ringing, a bell jingling, or thunder rumbling. So 鳴る means to sound or to ring. You know this because 鳴る can also be used for when your stomach rumbles: "rrrr" (る)!
The reading can come from 鳴く. So long as you know the reading for that word you can know the reading for this word as well.
電話が鳴る
the telephone rings
音が鳴る
a sound is emitted
アラームが鳴る
the alarm goes off
電話が鳴っている。
The phone is ringing.
ドアのベルが鳴った。
The door bell rang.
チャイムが鳴ったら、教室に入ってください。
When the bell goes off, please enter the classroom.