Translations:Phase velocity/26/en

Let us consider further the concept of propagation at constant phase and examine how this concept governs the propagation of any one of the sinusoidal waves, say, $u{\rm {=}}A{\rm {\ sin\ }}\left(k\left(x\pm vt\right)\right)$). Assume that the quantity v in this equation is positive, and choose the negative sign. Then the condition of constant phase is that $\varphi {\rm {=}}k\left(x-vt\right)\mathrm {=constant}$. This equation says that as t increases, x also must increase. Even when $x{\rm {<0}}$, so that $\varphi {\rm {<0}}$, the quantity x must increase - that is, it will become less negative. Thus, the constant-phase condition implies propagation in the increasing x-direction. Let us once more assume that v is positive, but now we choose the negative sign in the constant-phase condition. We get