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## Homework Statement

I have a system of infinite particles which when stationary are parted with distance a.

Their movement is described with

[tex]mu^{..}_{n}=\alpha(u_{n+1}+u_{n-1}-2u_{n}[/tex]

From which (assuming the solution is an harmonic wave) I got the dispersion:

[tex]\omega(k)=2\sqrt{\frac{\alpha}{m}}\left|sin(\frac{ka}{2})\right|[/tex]

where all the constants are given. One of the questions is:

"Find a frequency w over which the wave is a standing wave"

## Homework Equations

Form of the solution:

[tex]u_{n}(t)=ue^{i(kna-\omega(k)t)}[/tex]

## 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.