= Lennard-Jones chain sound speed
{c}
{title2=$v=\sqrt{72\epsilon/m}$}
A nearest-neighbour chain with the <Lennard-Jones potential> $V(x)=4\epsilon[(\sigma/x)^{12}-(\sigma/x)^6]$ has equilibrium spacing $a=2^{1/6}\sigma$ and <spring constant> $K=V''(a)=72\epsilon/a^2$. The <monatomic-chain dispersion relation> gives <speed of sound> $v=a\sqrt{K/m}=\sqrt{72\epsilon/m}$ and maximum <angular frequency> $2v/a$. The cancellation of $\sigma$ from the sound speed holds in this chain model; it does not remove the spacing from the cutoff frequency.
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