Charlie Brown is delivering the traditional whistle of appreciation for feminine beauty (though it usually has two notes: WEEEET-WOOO), and Patty takes offense. Schroeder, being more musical, delivers a mini-concert to Violet and gets to walk off with her. It is the melody to "Traumerei" from Schumann's "Scenes from Childhood" for piano.
Someone else already confirmed it, but here's a page with some trivia like that:
https://en.wikibooks.org/wiki/Annotations_of_The_Complete_Peanuts/Print_version
It's kind of hit-or-miss, but does list this one: