Cheetahs are unusual for a big cat in that they cannot roar. Perhaps the most well known of the sounds they do make is a chirp, which sounds rather astonishingly like a bird. This noise is used as communication between mothers and offspring, but has been observed in some other situations.
Cheetahs can also purr (in cats there is a purr versus roar dichotomy), hiss, and produce a number of other vocalizations. A "stutter bark" unique to males has been linked to the complexities of cheetah ovulation. Vocal-induced ovulation is not common in mammals, so it's no wonder keepers failed to figure out why their captive cheetahs weren't breeding.
Sources and Further Reading: National Wildlife Federation, National Geographic, Volodins Bioacoustic Group, Animal Diversity Web, Purring.org, An acoustic analysis of purring in the cheetah (Acinonyx jubatus) and in the domestic cat (Felis catus), A comparative acoustic analysis of purring in four cheetahs, A comparative acoustic analysis of purring in juvenile, subadult and adult cheetahs.