The Sea Whistle is an item obtained simply by progressing through the main story in both games. In Endless Ocean, the Sea Whistle is used to call to your partner, either from the gangplank of the Gabbiano or underwater (here, they don't respond very well), or call to wild dolphins/whales and get extra information on them. In Endless Ocean: Blue World, the Sea Whistle works a little better, and blowing it twice in a row commands your dolphin partner to look for whatever treasure they're best at finding.
Using the sea whistle on wild dolphins or whales will often unlock their trivia. This is because they rely heavily on sound to communicate, and as such a device that makes a sound tailored specifically to their ears (seen when your dolphin partners react so strongly to it) would garner a strong reaction (a pleasant one, in this case).
The Dragon Flute, from Endless Ocean: Blue World, may be an ancient, more powerful version of the Sea Whistle, as it is also known to influence species in the dolphin/whale taxon (the Singing Dragons, though it is not known what species they are yet, as they may be an entirely new one to science at the time that the game takes place). However, as the player can only use the Dragon Flute at certain points in the story and are unable to use it at any other time in order to test it out on regular dolphins and whales, it is unknown as to whether the flute is tailored specifically for the Singing Dragons or if it would affect other species as strongly as it does them. This may likely be the case, as any time the Song of Dragons has been sung, it was by a dolphin or a whale, and thus it may be simply a part of their genetic memory from a time when the Song was widely used as a method of taming dolphins or whales.