This is just the first part though. The real reward for this quest requires us to go above and beyond. We need a book of sheet music to get the best one. You might have found this somewhere else. There are 5 other books, but we're already here so lets get this one.

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Go back out to the atrium and look for the entrance to the living quarters on the ground floor. We need to get to the bathroom in the men's dorm. Move along the corridors. You should be in the women's area of the dormitory first. While you're here, keep an eye out for a terminal in the women's dorm area. You can hack the terminal and do a “noise flush” to kill all of the mirelurks in the dorm. If you're tired of fighting them, then do it. There's a lot of them up here, so it's usually a good idea.
Once you make it over to the men's side, you need to go to the bathroom in the back right corner. The book of sheet music is laying behind a toilet on the floor. Pick it up and then follow the arrows back out of Vault 92.
Agatha will thank you for the Soil Stradivarius. Giving this to her will open up her radio channel across the wasteland. I guess it's good if you want to listen to the violin while you play. We're mainly doing this for the second reward though. As a side note, you can sell to the violin to a few people, but that's a terrible idea.
Talk to her again and tell her that you found something interesting. She'll take the sheet music and thank you, but state that she doesn't have much for a reward. Do not be a hero! Politely say that anything she has will be fine. She'll offer you her husband's old magnum, Blackhawk. This is one of the best weapons in the game. It's very strong and has absolutely no recoil. It's basically a stronger version of Lincoln's Repeater. Congratulations, you're done.