The purposes of Ariel's songs are to calm Ferdinand. The first one actually calms Ferdinand and he also believes it calms the storm. .
Ariel's first song is about the calming of the storm. It is an invitation to dance upon the sands with him. Also, Ariel invites the spirits of the island to sing the chorus with him. Cockerels already crow and watchdog bark during the chorus anyway. In the second song, Ariel sings about life after death and how death is a good thing from the dead person's point of view. This is because Ferdinand believes his father (Alonso) is dead, and is mourning him. Both of Ariel's songs cheer him up and reassure Ferdinand.
Ferdinand and Miranda both react quite similarly to each other at the first sighting of each other. The other one astounds both of them. Miranda knows that there are no other people on the island apart from her and her father, so this surprises her. She does not think that he is human until he father assures her. When he tells her, she proclaims that he is good-looking and noble. .
Ferdinand is also surprised that there are people who were not on the ship were on the island. He is then even further surprised that Miranda is so beautiful. They fall instantly in love with one another.
All three characters of Prospero, Miranda and Ferdinand develop throughout the scene. To start with, Prospero is sensitive. He is telling his daughter of how they came to the island. He is acting all sorrowful and calm. As the scene goes on, Prospero starts to get more vicious (for example, when he giving Ariel instructions, being very bossy) and then he hits the point where he threatens with harsh punishment to Ferdinand and freezes him with a charm.
Miranda's character develops by getting more outspoken. She stays fairy quiet throughout the whole scene, but by the end she is asking more questions and getting interested in Ferdinand.
Ferdinand's character gets much more powerful. When he is faced with the storm on the boat, he follows the others while going to speak to the boatswain, but doesn't say anything.
