This is Proto Man.
There's a whole lot to his angsty story in the Mega Man universe, but I'm really not going to go into that here. In Mega Man 3 he just kind of appears every once in a while to fight you in a dead end for a few minutes and then he opens up a path for you to proceed. And his arrival is preceded by five very distinctive notes on a whistle.
But, if you've ever finished the game, you might know that there's more to the little ditty he plays. And, you can hear those extra notes pretty well any time you want, with a little timing.
So first, go to a stage where Proto Man appears, like Gemini Man's stage above. Then, once you get to the screen that Proto Man appears on, but before his song starts, hit the Pause button.
Done right (and you have an extremely small window of time to do it) the song will keep playing for a bit. Once it's done, unpause the game and then continue normally. And, this does work for both the original NES version and the Gamecube Mega Man Collection.
And, no, this isn't all that useful, really. But it is kind of neat, especially if you're a huge Proto Man fan... Those exist, right?