We can hear it, but we can't see it. The silence in the depths of the azure water is punctuated by the oddly tuneful sound of sonar and we dive in search of the owner of this eerily beautiful song.
Though it sounds close, the creature is playing with us and it's only when we emerge from the blue that we see an animal roughly the size of a bus break the surface for air not 20m away from the boat, which lurches to the side as everyone scrambles to get a better view of the magnificent humpback whale.
We're a few hundred metres out from the shoreline of Avarua, Rarotonga's town centre, so close we can see the trickle of tourists beginning to head down to the island's most famous drinking hole, Trader Jacks, which - if you don't want to dive - is also a pretty good place to watch whales blow, breach and splash around.
Our group is part of a Pacific Divers scuba expedition and we've enjoyed an incredible first day's diving in an area known as Edna's Anchor, a wide sand channel, flanked by coral-formed terrain, with a drop-off like a ski slope. Out deeper, around 22m, lie several old anchors, relics of the days when Rarotonga was thronged with whaling vessels rather than dive boats.
As the whale departs, we head back to shore for a cup of hot chocolate and a rest stop before our next excursion into water - the hue of which is other-worldly. The many shades of blue cause even our instructors, who dive in it daily, to comment on its lustre. Today's water temperature is 25C, leaving us warm in our shorty wetsuits; a bonus for those used to diving in New Zealand's cooler waters weighed down by hoods, booties and thick suits.
We motor out in Pacific Divers' custom-built boat to our second dive spot, the Coral Garden. Vast colonies of flower-like montipora coral give the site its name. Many other types of coral are well-represented here, too, and further out there are some wonderful open swim-throughs. We're told white-tip reef sharks are often lurking.
The warm water and 50m-plus visibility make diving so easy that we spend close to an hour underwater, soaking in the technicolour scenery and spotting ocean treasures including moray eels, turtles, rays and an array of vibrant, friendly fish.
The second day of diving is also sunny and we head out with the team at Pacific Divers to the wreck of the MV Mataora, an old Tongan cargo vessel now resting on the sea floor. She lies in 18m just off the reef to the north of the island.
Though the wreck has been broken up by a number of cyclones, this is a great place to see species such as lionfish and some beautiful coral.
After the usual rest stop on shore, it's back to business for our fourth and final dive at the spectacular Smurf City, which boasts no little blue men but an ancient coral seascape reminiscent of a field of giant mushrooms.
The highlight of this dive is an encounter with a large and extremely inquisitive turtle that swims up to one of the divers, Darryn, who watches in awe as it swims closer to his camera while he takes photos ... until he starts wondering whether it intends to eat his camera for lunch.
Diving done, we're tired and ready for an afternoon beverage or two at Trader Jacks.
Back at the base, the friendly team at Pacific Divers takes care of the admin; washing scuba gear and unloading tanks and gear from the truck.
Toasted-cheese sandwiches are handed around and then we head off into the sunshine, armed with some whale-sized tales of sea creatures, great and small, and looking forward to doing it all again next time.
Further information: See cookislands.travel.
Haley McCrystal dived in Rarotonga under her own steam.