很显然which是多余的,which一般用在定语从句中,引导定语从句,但这句话没有先行词,也不是定语从句,就不需要which.
正确的句子应该是：
They soon became popular with their beautiful voice.
他们不久就凭借自己优美的嗓音而受到欢迎.那改成the voice with which they soon became popular呢，是不是要加逗号呢你如果这么改的话和原来的意思就不一样了，原来的句子the voice 作介词宾语，你要这么改，只有主语，没有谓语了，他们因之而出名的嗓音，后面就没有内容了，怎么样啊？你看看这样可以吗？The voice with which they soon became popular is very beautiful. 他们借之而出名的嗓音非常好听。