All big cats roar (except for snow leopards), but they don’t typically purr (except for cheetahs). Small cats purr, but can’t roar. This is due, in part, to a small bone in the neck called the hyoid. In big cats, this bone is flexible, but in small cats, it is rigid. The big cats also have flat, square vocal cords, and a longer vocal tract that allows them to make a louder, lower sound with less effort. In small cats, the hardened hyoid combined with vocal folds are believed to create the purring sound.
