Wave
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the general n-dimensional wave equation
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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
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there exists two solutions propagating in opposite directions of the system namely
Solutions for systems of different geometries
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Generally we expect a harmonic solution in the form of
where
is the wave vector and
is the phase of the system
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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
