What is the ruling on money earned from programming an application to teach the Arabic language to non-native speakers, if the application includes 12 seconds of music at the beginning of each educational chapter, which the user can skip?

It is obligatory to stipulate that the lessons be free of music. If that is not possible, then there is no harm in programming an application that contains a small amount of music at the beginning of the lessons, because the intention is to teach the language, not the music. What is tolerated incidentally in something is not tolerated intentionally, just as a small amount is tolerated and excused to alleviate hardship, and the widespread affliction of music necessitates leniency, for "when a matter becomes difficult, it expands."