The propagation of harmonic waves in a linear chain consisting of equally spaced
masses m connected by linear springs of stiffness k has been studied extensively. The
chain behaves as a low pass filter so that waves can propagate without attenuation
below the frequency . Above this frequency, the amplitude decays
exponentially and those waves are called evanescent waves. The frequency range is called a pass-band and in that range the dispersion relation is given by , where k is the wave number, and a is the distance between two consecutive masses. In that range, waves with different phase velocities and group velocities .
For long waves , the chain behaves as a rod governed by the classical wave
equation. Several higher order continuum models are derived from the dispersion
relation.
Comments
Leave a comment