The flow-induced pulsations in corrugated pipes result from a feedback loop between an acoustic resonator and the noise amplification at each shear layer in the axisymmetric cavities forming the corrugations. The quality factor of the resonator is determined by the reflection coefficients at the ends of the corrugated pipe and by the damping in the pipe. In this work, the damping of acoustic waves in a set of smooth and corrugated pipes is measured by a direct method. For these measurements, the tested pipes are placed between two measuring pipes equipped with flush-mounted pressure transducers to allow reconstruction of the acoustic waves with the two-microphone method. Loudspeakers are used to generate acoustic waves, and anechoic terminations allow near reflection-free conditions. The tests are done in air without flow and with flow velocities up to 60 m/s. The results for the corrugated pipes allow to investigate the influence of the corrugations on the damping. Two cases are considered: Without flow, the visco-thermal damping is increased for the corrugated pipe compared to a smooth pipe of same diameter. When there is a flow in the pipe, the damping results depend strongly on the flow velocity. At certain frequencies which depend on the flow velocity, the damping increases or decreases. The regions of increase or decrease are shown to be at constant ranges of Strouhal numbers. The decrease of the damping can in some cases be such that acoustic waves are amplified through the corrugated pipe. This corresponds to the acoustic source behavior of the shear layers. The measured amplification is compared to the computed source term due to the axisymmetric cavities.