= Sound speed and inferred plane spacing
Reading near the origin, an acoustic point is approximately $(q,\omega)=(1.9\times10^9\,\mathrm{m^{-1}},0.9\times10^{13}\,\mathrm{s^{-1}})$. The initial slope therefore estimates
$$
\boxed{v_s=\left.\frac{d\omega_-}{dq}\right|_{q=0}\simeq4.7\times10^3\,\mathrm{m\,s^{-1}}}.
$$
Combining the slope with the inferred <spring constant> gives
$$
\boxed{a=v_s\sqrt{\frac{m_A+m_B}{2\alpha}}\simeq2.0\times10^{-10}\,\mathrm m=0.20\,\mathrm{nm}}.
$$
This $a$ is the model's adjacent Na-plane to Cl-plane spacing; its cell length is $2a$. The slope is a graphical estimate, so values around $4.5$–$5.0\,\mathrm{km\,s^{-1}}$ and spacings near $0.2\,\mathrm{nm}$ are consistent with the reading precision. A real ionic crystal has interactions beyond the scalar nearest-neighbour model; an intercept-and-slope fit need not reproduce the entire measured dispersion or independently measured structural spacing exactly.
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