Have your Arduino play the song "Twinkle Twinkle Little Star" through a buzzer.

You don't have to play the whole thing; the first four measures will do (which translates to the first 14 notes in "Twinkle Twinkle Little Star").

Here is the sheet music to the song. If you are not familiar with how to read sheet music, you can learn the basics here.

Once you know which notes go where in the song, a table like this will be helpful in determining which frequencies to play in the tone() function.