"It's odd, because he usually gives us a reason why we're not allowed to go somewhere –– the forest's full of dangerous beasts, everyone knows that. I do think he might have told us prefects, at least."
"And now, before we go to bed, let us sing the school song!" cried Dumbledore. Harry noticed that the other teachers' smiles had become rather fixed.
-- Harry Potter and the Sorcerer's Stone by J.K. Rowling
What does smiles become fixed mean?
(1) They all are happy enough to keep their smiles.
(2) They become nervous after the headmaster’s notice, the third-floor corridor is out of bounds. For it suggests protecting philosopher’s stone, and it also means imminent attack for it from You-Know-Who.