Surface True and Leaky Waves in Subsonic and Supersonic Regions. Explicit Solution of a Simple Model

D. Trzupeka, b and P. Zielińskia, c a The H. Niewodniczański Institute of Nuclear Physics PAN, Radzikowskiego 152, 31-342 Cracow, Poland b Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Cracow, Poland c Institute of Physics, Cracow University of Technology, Podchorążych 1, 30-084 Cracow, Poland

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A simple model of a surface of a 2D continuum is shown to exhibit subsonic and supersonic surface resonances (leaky waves, pseudosurface waves), i.e. finite lived excitations, along with usual surface waves (true subsonic surface waves). The physical meaning, controversial in the existing literature, of the surface leaky waves in both regions is discussed by a thought experiment in which a stimulus adjusted to the resonance parameters is applied to the surface. The infinite displacement stimulus ratio in the long time limit then is shown to be in power in all the cases of surface states and a finite amplitude of the leaky waves is demonstrated despite an apparent divergence suggested by their algebraic form.

DOI: 10.12693/APhysPolA.117.570 PACS numbers: 63.20.D-, 68.35.Ja