Eigenmodes of fractal drums: A numerical student experiment

• DOI: 10.48550/arxiv.2309.13613
• Publication Date: 2023-01-01
• Authors: Veronica P. Simonsen; Nathan Hale; Ingve Simonsen
• Keywords: Mode (computer interface)

``Can one hear the shape of a drum?'' was question posed (and made famous) by mathematician Mark Kac in mid-1960s. It addresses whether deeper connection exists between resonance modes (eigenmodes) drum and its shape. Here we propose numerical experiment, suitable for advanced undergraduate physics students, on calculation eigenmodes square Koch fractal drum, which experimental results do exist. This exercise is designed to develop students' understanding vibrations drums, their eigenmodes, potentially integrated density states. The students calculate lowest order visualize these modes, study symmetry properties. As an extension, may investigate states compare findings Weyl-Berry conjecture.