= Solution
The supplied <Speed of sound>[sound speed] determines the spring-to-mass ratio without needing either parameter separately:
$$
\sqrt{C/m}=\frac{v_s}{a}=\frac{4.0\times10^3}{2.0\times10^{-10}}=2.0\times10^{13}\ \mathrm{s^{-1}}.
$$
Consequently
$$
\boxed{\omega(k)=4.0\times10^{13}|\sin(ka/2)|\ \mathrm{rad\,s^{-1}},\quad
k_{\rm edge}=\frac\pi a=1.571\times10^{10}\ \mathrm{m^{-1}}.}
$$
The curve is even in $k$, rises linearly from the origin with one-sided slopes $\pm4.0$ km/s, and flattens at both <Brillouin zone>[zone edges]. Its maximum is $\omega_m=4.0\times10^{13}$ rad/s, or ordinary frequency $\nu_m=\omega_m/(2\pi)=6.366$ THz. Keeping <angular frequency> distinct from cycles per second avoids a factor-of-$2\pi$ error. Repeating the curve outside the first zone is a representation of equivalent <crystal> momenta, not the discovery of additional modes.
\Image[/past-exam-of-the-condensed-matter-physics-course-of-the-university-of-oxford/2016-monatomic-chain-dispersion.png]
{title=Positive-frequency acoustic dispersion of the specified monatomic chain}
{description=Original nearest-neighbor harmonic-chain calculation, with both propagation directions in one first Brillouin zone. The plotted vertical frequency is angular frequency.}
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