What is Rossby wave; upper-level trough and ridge?

Example 22.6 (Three waves at 45° N)

With $\Omega = 7.292 \times 10^{-5}\,\mathrm{s}^{-1}$ (a sidereal day of $23.9345\,\mathrm{h}$) and $a = 6371\,\mathrm{km}$, $\beta = 1.62 \times 10^{-11}\,\mathrm{m}^{-1}\,\mathrm{s}^{-1}$ at $45{}^{\circ}$ N. In a westerly of $15\,\mathrm{m}/\mathrm{s}$, a wave of $4000\,\mathrm{km}$ has $\beta/k^2 = 6.6\,\mathrm{m}/\mathrm{s}$ and moves east at $8.4\,\mathrm{m}/\mathrm{s}$; one of $6000\,\mathrm{km}$ has $\beta/k^2 = 14.8\,\mathrm{m}/\mathrm{s}$ and barely moves, at $0.2\,\mathrm{m}/\mathrm{s}$; one of $8000\,\mathrm{km}$ moves west at $11.2\,\mathrm{m}/\mathrm{s}$.