 Horizontal phase velocity

For phase $kx+mz-\omega t$ with $k\ne 0$, hold $z$ fixed: a contour of constant wave phase advances in $x$ at $\omega /k$. This is the speed at which a tilted wavefront crosses a horizontal line. It differs from the horizontal component of the vector phase velocity, $\omega k/(k^2+m^2)$, which is defined along the wavevector.