Isospectral Drums
Striking a drum excites a spectrum of vibration modes that together make up the instrument’s characteristic sound or acoustic signal. These vibration modes correspond to the eigenmodes, or eigenfunctions, of the drum’s membrane. Thus you can study this problem by solving eigenvalue problems for stretched membranes.Two different geometric shapes are modelled, with all other parameters being equal. If you can find two differently shaped membranes that have identical eigenvalues—in other words, they are isospectral—then it’s not possible to “hear” the shape of a specific drum.
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First eigenmode for one of the drums. |
Engineering Fields
- Equation-Based Modeling
- Benchmarking Studies
Application Areas
- Numerical Analysis, PDE, FEA