The judges did not take long yesterday afternoon in deciding to give George Rochberg's "String Quartet No. 4" first place in this year's Kennedy Center Friedheim Awards.

The five new American chamber works, which had been selected from 97 entries for public performance, were played in alphabetical order. As it happened, Rochberg's quartet was presented last. From the opening measures it was clear that we were hearing music that entered regions no one else that afternoon had touched.

For some time now the 61-year-old Rochberg, who was the only widely known figure among the five finalists, has been seeking to come to terms with the past without completely abandoning the developments of this century. In this quartet, which is one of a set of three written for the members of the Concord String Quartet, he seems to have at last found the synthesis he was seeking.

The language is rich, powerful and complex. Long, poignantly beautiful melodies are punctured by sharp, staccato outburtsts. Passages of classic simplicity are followed by harsh, dense textures.The music stands as a metaphor for the conflict between impersonality and feeling that plagues contemporary life.

Rochberg's first prize carried with it a cash award of $5,000.Second place and $2,000 went to Claude Baker's "Banchetto Musicale," a work heavily dependent on the music of George Crumb. Third place and $500 went to Claus Adams' "String Quartets," a well-written, idiomatic work that string quartets will derive much pleasure from playing.

The other two works in the finals were Peter Lieberson's vital "Tashi Quartet," which deserved better, and Bruce MacCombie's witty "Parkside Music."

Performances in every case were of the kind composers dream of and seldom get-- dedicated, knowledgeable and passiionate. Judges for the awards were Irving Lowens, Boris E. Nelson and Thomas C. Willis.