Abstract
The Helmholtz equation with hybrid (mixed) boundary conditions is solved for the first time for the basic circular and rectangular regions. The solution applies to elastically attached membrane vibrations and acoustic or electromagnetic waves in hybrid (neither soft nor hard) walls. It is found that the fundamental vibrational mode is always symmetric and decreases singularly to zero as the hybrid parameter tends to the hard wall limit. An important result is that, since no boundary can be ideally hard, there always exist a low frequency mode which corresponds to the true cut-off frequency. This is important for acoustical, optical or electromagnetic wave guides.
Published Version
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