Whose experiments cracked the DNA and discovered unequivocally that a genetic code is a "triplet""?"

George Gamow had proposed that the code should be a triplet, since 4 bases must code for 20 amino acids ($4^3 = 64$).
Marshall Nirenberg's cell-free system for protein synthesis finally helped the code to be deciphered: Nirenberg and Matthaei used a synthetic poly-U mRNA and obtained a polypeptide of phenylalanine, showing that UUU codes for phenylalanine.
This work established experimentally that the code is a triplet.
Beadle and Tatum proposed the one gene–one enzyme hypothesis; Hershey and Chase proved that DNA is the genetic material; Morgan and Sturtevant worked on linkage and gene mapping.
Hence the answer is Nirenberg and Matthaei.