Can you hear the shape of a drum?

Date of Completion

January 1998


Health Sciences, Audiology|Psychology, Experimental|Psychology, Cognitive




Kac (1966) first poised the question of whether spectral data radiating from vibrating plates could be rich enough to specify the geometry of the plates. Recently, mathematical proofs have shown the existence of isospectral companions-manifolds of differing geometries that produce identical spectra-leading some to conclude that the perception of manifold shape based on spectral data may not be possible (e.g. Gordon & Webb, 1995). In six experiments, the present dissertation examines this issue by asking human participants to hear the geometric dimensions of thin, isotropic plates set into free vibration. Experiments 1, 2, and 5 revealed that the perceived height and width of thin rectangles of various material compositions and constant surface area are a single-valued function of G, the invariant parameter of the two-dimensional wave equation. Experiments 3 and 6 revealed that the geometry of thin circles, triangles, and rectangles of a variety of material compositions are perceptible by hearing. Lastly, Experiment 4 revealed that the perception of hardness of a variety of materials is also a function of G. These results are discussed in the context of a general theory of shape perception and the specificational link between perception and the physical properties of the perceived world. ^