It all depends upon the child's grade & his/her ability to concentrate on his/her studies. It also depends upon the TYPE of music h/she is listening to. Sometimes hard rock 'n' roll music can be quite distracting to studying w/the child concentrating more on the music than his/her studies. Listening to classical music can be quite conducive to studying. However, it is best for children to study in a noise-free environment.
I remember as a teenager, my parents strictly forbade me to study while any type of music was one. Their mantra was to do only one thing at a time. If one was watching television, watch television. If one was reading, read etc.