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Why is the phase velocity of waves on a rope independent of the wave length?
A rope is described by the wave equation
$$ (\partial_t^2 - \partial_x^2) \, \varphi = 0 $$
It is well known that there is no dispersion for resulting wave solutions. This implies that all plane waves ...
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Why does the phase velocity of a string attached to springs depend on the wave length?
A string can be described by the wave equation
$$ (\partial_t^2 - \partial_x^2) \, \varphi = 0 $$
while a string attached to a spring (i.e. with a harmonic restoring force) at each location is ...
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