Karen Hesse's The Music of Dolphins is a adolescent, science-fiction/fantasy novel. It was published in 1996 by Scholastic Publishing.
Hesse does not specifically give a time period during which the story of Mila takes place. Instead, she offers readers a couple different clues as to suggest the time period.
First, Mila arrives on an island near Cuba as the result of a plane crash (which happened when she was a young girl). Therefore, this event had to happen after the creation of passenger planes. Therefore, the story must take place after 1919 when the first passenger planes were established.
The second clue readers are given comes in the form of the helicopter which sees Mila and "rescues" her. Helicopters became very successful during the 1930s.
Another clue which one could use to determine when the novel takes place is the study of language with feral children. Feral children have been "captured" and taught since the 14th century. While some of the cases shown that early have not been well documented, other more recent cases have. One can find very prominent cases of feral children being taught language skills beginning in the 1940s.
The names in the novel offer one last clue to a time period. Shay is another feral child being taught with Mila. Shay was a name which was popular in 1991. Justin was a popular name for boys in 1988. Sandy was a popular name in 1960.
Taking all of the information into consideration, one could assume that the novel takes place after the 1940s.