\(\Delta \lambda=\frac{\lambda^2}{L}=\frac{6328\overset\circ A }{10km}=4*10^{-17}m\)

\(\Delta \nu=\frac{1}{\tau_0}=\frac{c}{L}=\frac{3*10^8m/s}{10km}=3*10^4 Hz\)