My textbook states the following: The wave disturbance travels from x=0 to some point x to the right of the origin in an amount of time given by x/v, where v is the wave speed. So the motion of point x at time t is the same as the motion x=0 at the earlier time t-(x/v). Hence we find the displacement of point x at time t by simply replacing t in the equation: y(x=0,t)=Acos(wt) by (t-(x/v)) to get the following: y(x,t)=Acos(w(t-x/v)) . My book is talking about sinusoidal waves and how to give them a function. I dont understand the t-(x/v) part.... it says that "motion of point x at time t is the same as the motion x=0 at the earlier time t-(x/v)".... what does it mean by motion? Does it mean that its at the same phase of the sin wave? This wouldnt make sense because if the x displacement is not a factor of 2pi, then it would be in a different phase.... Can someone please clarify this part?