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The discovery of quasi-periodic atomic order in the crystalline state has uncovered an exciting new class of symmetries that has never been explored before. Because of their non-periodic translational order and self-similar properties, quasi-periodic structures offer unique opportunities for investigating questions related to their acoustical behavior. Their unique long-range non-periodic formations have the ability to diffuse and orchestrate the flow of sound energy in many unique ways; offering intriguing potential for innovating a new wave of optimized sound diffusers. One key limitation with available periodic diffusers is that their repeating logic creates repetitive energy loops, which significantly reduce their ability to uniformly disperse sound energy. Quasi-periodic geometry can mitigate such limitation. By encapsulating an infinite variety of distinct profiles in all directions, quasi-periodic surfaces can eliminate the formation of bundled or looped reflections; considerably enhancing the ability of the diffuser to uniformly disperse sound energy. To investigate this hypothesis, an experimental approach is used to simulate sound reflection patterns of the quasi-periodic surface profiles using a ray tracing method. Both qualitative and quantitative analyses are used to interpret the simulated results. The international Standards (ISO) metrics are used to validate the proposed approach and verify the results. Results show that the diffusion quality of the tested quasi-periodic surface is superior to the diffusion performance of the tested periodic surface.
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