Book that talked about the language of dolphins (before the science confirmed it)?

Dolphin Island by Arthur C.Clarke, 1963

Late one night (in the world of the future), a giant cargo hovership makes an emergency landing somewhere in the middle of the United States and an enterprising teenager named Johnny Clinton stows away on it. A few hours later, the craft crashes into the Pacific Ocean. The crew ("even the ship's cat") is offloaded onto lifeboats, leaving Johnny (who, as a stowaway, was not on the ship's manifest) adrift in the flotsam from the wreckage. His life is saved by the "People of the Sea"—dolphins. A school of these fantastic creatures guides him to an island on Australia's Great Barrier Reef. Johnny becomes involved with the work of a strange and fascinating research community where a brilliant professor tries to communicate with dolphins. Johnny learns skindiving and survives a typhoon—only to risk his life again, immediately afterwards, to get medical help for the people on the island.

Based on a positive comment, I'm going to suggest this might be The Jonah Kit (1976) by Ian Watson. One of the threads of the book concerns a sperm whale that has had the mind pattern of an astronaut imposed on it so the whale can communicate with humans and be controlled/directed. (The whale seems to be forced to do things it would not wish to, like surfacing periodically to report on what it has seen in the deeps.)

Sound, echoes, and sound pictures seem to be a large part of how the whale is portrayed to think and communicate with its kind.

He compares his mental model of a Ten-Arms reaching up to wrap suckers round his forehead-a painful memory, this!-with one of a Steel cruising a deep trench: a pregnant Steel, with a dozen steel foetuses upright in womb pods along her back. (Curiously rigid and lifeless, though, her little ones-for all that there's a tiny heart tick present in each of them...!)

He searches peaks and canyons far below, building him-self an exact sound model of the crags and depths, the water density gradients, deep scattering layers of crustaceans, jellyfish, siphonophores, that billow out around the mountains in faint veils. A percussion of croaks, drummings and grunts stipples his echo map too, from other small food beasts making noises.

When Seven gather nose to nose and brow to brow in slack water, waving their flukes to stay in place, their seven melons of liquid wax cut off from the sea-world and look inward, not outward; become a closed system for their clicking thoughts. The pure ideas burst-pulsing in each other's melons echo, re-echo, combine and interfere... weave patterns larger than the pattern of an idea carved in oil-wax in any single brow. So the Glyphs of Awareness are born-which only a new Star-Gathering can fully open up again, which nonetheless finger on in the individual's memory in the meanwhile as foci.

I am throwing in the book the movie "The Day of the Dolphin" was based upon.

https://en.wikipedia.org/wiki/The_Day_of_the_Dolphin_(book)

The Day of the Dolphin (Un animal doué de raison – lit. A Sentient Animal) is a 1967 science fiction thriller novel by French novelist Robert Merle. The plot concerns dolphins that are trained to communicate with humans, and their use in warfare. The central character is a government scientist with similar ideas to those of John C. Lilly.

The English translation of the novel was published in 1969 with the title The Day of the Dolphin, which is not a literal translation of the French title. The novel was the basis for the 1973 film The Day of the Dolphin, though the film's plot was significantly different from that of the book, even in inconsequential details. For instance, in the book, the dolphins are named Ivan ("the terrible") and Bessie and call themselves Fa and Bi; in the film, they are instead named Alpha and Beta and call themselves Fa and Be.

It fits the timeframe. I have not read the book, but I remember the movie and there were discussion about the dolphins' language, even if in the movie they made the dolphin understand English.