What is the ruling on buying new headphones for my brother after accidentally breaking his old ones, knowing that he uses them to listen to music?

As long as the damaged headphones can be used for a permissible purpose, compensation for their destruction is obligatory because they hold a permissible benefit. They are not like things that are used only for unlawful purposes. The fact that the destruction occurred by mistake does not negate the obligation of compensation, as error and intent are the same concerning compensation for people's property.