The realization of Landau levels with a high density of states has recently attracted considerable attention in wave systems. Since classical waves are inert to real magnetic fields, researchers have adopted a purely geometric approach to design pseudomagnetic fields (PMFs) by shifting twofold Dirac cones in momentum space. Here, we extend the twofold Dirac cone case and demonstrate acoustic Landau levels based on a gradient acoustic crystal with a fourfold Dirac cone. By linearly tuning a dimensionless factor, we generate two PMFs with identical amplitudes but opposite directions, thereby obtaining twofold degenerate acoustic Landau levels. Through measurements of the total energy spectra of the gradient acoustic crystal, we experimentally demonstrate the existence of these acoustic Landau levels. Furthermore, we demonstrate one-way sound propagation of the associated pseudospin-dependent edge states using two types of chiral sound sources and verify their robustness by introducing two types of defects. The observed twofold degenerate acoustic Landau levels and their corresponding pseudospin-dependent edge states may have potential applications in sonic lasers, enhancing sound emission, and nonlinear wave mixing.

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• Acoustics
• Geometric & topological phases
• Landau levels
• Honeycomb lattice