In the lecture notes on waves, we have shown that the waves on a plucked guitar string are transverse standing waves consisting of a linear superposition (i.e. sum) of harmonics of the fundamental (first harmonic) with the fundamental itself. A first-order mathematical description of the shape of the overall waveform of the transverse standing wave on a plucked guitar string is a triangle, or s...

The advent of transformation optics and metamaterials has made possible devices producing extreme effects on wave propagation. Here we describe a class of invisible reservoirs and amplifiers for waves, which we refer to as Schrödinger hats. The unifying mathematical principle on which these are based admits such devices for any time harmonic waves modeled by either the Helmholtz or Schrödinger ...

Compact, time-harmonic, acoustic sources produce waves that decay too slowly to be square-integrable on a line away from the sources. We introduce an inner product, arising directly from Green’s second theorem, to form a Hilbert space of these waves and present examples of its computation. c © 2005 Wiley Periodicals, Inc.

Elastic waves in materials with cylindrical orthotropy are considered, this being a plausible model for waves in wood. For time-harmonic motions, the problem is reduced to some coupled ordinary differential equations. Methods for solving these equations are discussed. These include the method of Frobenius (power-series exapansions) and the use of Neumann series (expansions in series of Bessel f...

Time-harmonic waves are scattered by obstacles, through which waves can also travel. Various examples from acoustics, elastodynamics and electromagnetics are discussed, including imperfect interfaces, chiral materials and wood. The paper gives a very subjective overview but with emphasis on the contributions and influence of Ralph Kleinman.