Can someone explain why で particle is used with 鳴る in the following sentence?
ケータイが大きなおとで鳴っています。

sentence is taken from JLPT4 book

質問を翻訳

「で」goes with a word or a sentance that means supecific conditions before it in many case, in your case the condition is 大きな音.
For instance,
商品が高値で売られている。（高値 is the condition. 高値で is "at a high price"）
私は車で来た （車 is the condition, 車で means "by car"）
if you don't know if it is a condition or not, let's see if the sentanse works when you omit the condition. if it works it means what you omtted was the condition.