(CBS News) RAROTONGA -- Rarotonga, one of the Cook Islands in the South Pacific, is a meeting place for humpback whales. The humpback was hunted nearly to extinction, but after the whaling ban in 1966, they are once again swimming in every ocean.
On assignment for "60 Minutes," we met a human who may know them best: American marine biologist Nan Hauser.
Eighty percent of their lives are spent submerged, and this is where Hauser has made her most beautiful discoveries.
"Here, we see a male standing on his head, upside down, singing a song," Hauser says. "They are motionless, and the song bellows out."
The humpback song can be 20 minutes long, and they repeat the same song again and again. Males in one region will all sing the same song the same way, but next year, they'll return with a new composition.
The songs are air moving around inside their heads. It makes the sound, even though the whales don't have vocal cords.
"It's almost, I think, like taking a balloon full of air and going --" Hauser pretends to stretch a balloon.
The sound carries for miles, and Hauser believes it's all to mark territory.
"They take turns singing, perhaps to say, 'My lungs are bigger. I can hold my breath longer. I can sing a more beautiful song. I'm the dominant male. I'm going to sing here, so you move away and sing somewhere else,'" Hauser says.
Watch: Whales come close to swallowing divers, below.
"I think the most common whale sound is --" Hauser imitates a whale song. "But we get everything. We've even had the laughing monkey, 'Ee, ee, ee, ee.' Creaky doors."
Hauser says scientists don't know what the whales are saying, acknowledging she speaks whale, but doesn't understand it.
There will be much more about diving with the humpback whales this Sunday on "60 Minutes."