Resonances of three transverse standing-wave modes in a waveguide with periodic wall undulations

•We investigate the interactions of three transverse modes in a periodic waveguide.•Three mode resonances result in the splitting of the traditional forbidden band.•We find the transparency of the forbidden band to a single high-order mode.•The transmission losses of two ducts illustrate the transparencies in the gaps.•The radial distributions and their fittings show the purity of the generated modes.

Interactions of three transverse modes are investigated in a waveguide with periodic walls. Resonances of two guided wave modes always result in forbidden bands for wave propagations when the wavenumber matching conditions are satisfied. As a third mode is involved due to the selected wall corrugations, we find that a single high-order mode can penetrate through the forbidden band based on the complex interactions. A method for generating a single high-order transverse mode is proposed by manipulating the multimode interactions. The numerical simulations on acoustic waveguides, showing the extreme suppression of the unwanted modes in the Bragg and non-Bragg gaps, demonstrate the validity and the efficiency of the proposed method.