"She is going to hear the music."
Translation:Ella va a escuchar la música.
"Escuchar la musica" y "Oír la musica" both are correct because both cases exist. If the case was the one you mention, I agree "oír" would be better, because the person in the other room wouldn't voluntarily be listening to the music. The difference between "oír" and "escuchar" is very slight. It is not the same "Oír a alguien hablar" que "Escuchar a alguien hablar". In the first one you're just aware that someone is speaking, you're probably not involved in the conversation; in the second one you're probably part of the conversation and actively paying attention to what the person is saying :)