2018-11-02

Wave

• the general n-dimensional wave equation

• where in the special case of travelling in a tight string, an erroneous but good for practical purposes derivation shows

• this is the dispersion relation for a one dimensional non-dispersive wave equation

• there exists two solutions propagating in opposite directions of the system namely

Solutions for systems of different geometries

• Generally we expect a harmonic solution in the form of

• where is the wave vector and is the phase of the system

• In 2D, e.g. a drumskin we get the normal form of a harmonic wave solution

  Plane wave

  Spherical waves

  Cylindrical waves

Elliptical polarization

• For a wave travelling in the positive x direction

• We usually exclude the time dependent terms for simplicity in notation.

• By convention, looking against the propagation direction of the wave, define the