The method of multiple scales is employed to analyze the wave propagation in a rectangular hard‐walled duct whose walls have weak periodic undulations. Interacting modes traveling in the same direction propagate unattenuated. The energy is continuously exchanged between the two modes. The modes that travel in opposite directions are attenuated and, there, may be cut off. This cutoff will depend upon the geometry of the cross section as well as the phase‐angle differences between the undulations of the opposite walls.