I have a system of infinite particles which when stationary are parted with distance a.
Their movement is described with
From which (assuming the solution is an harmonic wave) I got the dispersion:
where all the constants are given. One of the questions is:
"Find a frequency w over which the wave is a standing wave"
Form of the solution:
The Attempt at a Solution
I found out that I can bound k to the interval [-2pi/a,+2pi/a]
(for every other k there's a corresponding k in the interval, for which the solution is the same)
But I have no idea what to do next
but maybe if for some k, w(k)=-w(-k) then summing the wave k and wave -k, will
result in a standing wave. But the only k that satisfies this is k=0, for which there is no wave at all.