The title refers to the musical "The Sound of Music" which opened on Broadway (New York City) at the Lunt-Fontanne Theatre on November 16, 1959, ran for 1443 performances and won (in a tie) the 1960 Tony Award for the Best Musical.
The show's closing credits indicate that "Robbie's award-winning song" had words by the episode's writers, Ed James & Seaman Jacobs, and music by Don Grady - Robbie.