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

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.