= Solution
Assume a cold, unmagnetized, weakly collisional <plasma>, a small fractional bandwidth and $\omega\gg\omega_p$. The <dispersion relation> is $\omega^2=c^2k^2+\omega_p^2$, with $\omega_p^2=n_ee^2/(\epsilon_0m_e)$. The <group velocity> and propagation time are
$$
v_g=\frac{d\omega}{dk}=c\sqrt{1-\frac{\omega_p^2}{\omega^2}},\qquad
\tau(\omega)=\frac Lc\left(1-\frac{\omega_p^2}{\omega^2}\right)^{-1/2}
\simeq\frac Lc\left(1+\frac{\omega_p^2}{2\omega^2}\right).
$$
The lower frequencies arrive later. Taking the magnitude of the frequency derivative over $\Delta\omega$ gives
$$
\boxed{\Delta\tau\simeq\frac{L\Delta\omega}{c\omega^3}\frac{n_ee^2}{\epsilon_0m_e}.}
$$
For a nonuniform line of sight, replace $n_eL$ by the <dispersion measure> $\int n_e\,dl$. The light travels at the <group velocity>, not at the <phase velocity>.
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