Elephants can communicate using sounds below the range of human hearing ("infrasounds" below 20 hertz). It is commonly speculated that these vocalizations are produced in the larynx, either by neurally controlled muscle twitching (as in cat purring) or by flow-induced self-sustained vibrations of the vocal folds (as in human speech and song). We used direct high-speed video observations of an excised elephant larynx to demonstrate flow-induced self-sustained vocal fold vibration in the absence of any neural signals, thus excluding the need for any "purring" mechanism. The observed physical principles of voice production apply to a wide variety of mammals, extending across a remarkably large range of fundamental frequencies and body sizes, spanning more than five orders of magnitude.