# Wave disturbance conceptual question

My book states:

The wave disturbance travels from $x = 0$ to some point $x$ to the right of the origin in an amount of time given by $t=\frac{x}{v}$, where $v$ is the wave speed. So the motion of point $x$ at time $t$ is the same as the motion of point $x = 0$ at the earlier time $\left(t - \frac{x}{v}\right).$

I do not really get why it says to use negative $\frac{x}{v}$ when the sinusoidal wave is moving to the $+x$ direction.

Why is it that?

It is basically a notation to represent a sinusoidal wave (which is travelling in $+ x$ direction ) in the form : $\sin(wt-kx)$. Had the wavefunction been $\sin(wt + kx)$ the wave function would correspond to a wave travelling in a $-x$ direction. So it's only a notation as far; nothing so conceptual about it.
• @Aniket: There may be a CONCEPT but that is not deep. It is just shifting of the graph; that's it.
The wave travels to the right, so a disturbance that passes x=0 at t=0 arrives at point x (>0) at a later t>0. I can "predict" the motion of the wave at point $x$ by looking back in time - what was the wave doing at an earlier time at the origin? Since the disturbance travels at velocity $v$, we know how long ago it passed an earlier point. And that is the meaning of the $-\frac{x}{v}$ term, and the reason you need the negative sign.