In 1971 Zel'dovich predicted that quantum fluctuations and classical waves reflected from a rotating absorbing cylinder will gain energy and be amplified. This key conceptual step towards the understanding that black holes may also amplify quantum fluctuations, has not been verified experimentally due to the challenging experimental requirements on the cylinder rotation rate that must be larger than the incoming wave frequency. Here we experimentally demonstrate that these conditions can be satisfied with acoustic waves. We show that low-frequency acoustic modes with orbital angular momentum are transmitted through an absorbing rotating disk and amplified by up to 30% or more when the disk rotation rate satisfies the Zel'dovich condition. These experiments address an outstanding problem in fundamental physics and have implications for future research into the extraction of energy from rotating systems.