How is x-vt a rightward moving wave?

[Jaccobtw]

Homework Statement

How is x-vt a rightward moving wave?

Relevant Equations

f(x-vt) = disturbance

The only way I can see x-vt being a rightward moving wave is if x-vt = some position the wave had initially. As t increases, x-vt gets smaller, despite the fact that it is a rightward moving wave. For example, if x = 10 m and v = 1 m/s, as t increases, x-vt describes a position the wave had in the past. Is this correct intuition?

 

[PeroK]

It's a rightward moving wave for $v > 0$. At $t =0$, the wave takes the form of $y = f(x)$. Choose a function $f$. Something simple. For example $f(x) = x$. Draw that initial state of the wave on a graph.

Then, for $t = 1$, say, the wave takes the form $y = f(x -v) = x -v$. Draw that state of the wave on a graph. Take $v = 1$ as well, so that $y = x - 1$.

Has the wave moved left or right?

 

[kuruman]

Another way of looking at this is from the standpoint of the wave.

For positive $x$ at a particular instant in time $t$ and at position $x$, the function $f(x-vt)$ return a specific value, say $3$ units. Time always increases. At a later time $t'>t$ must $x$ increase, decrease or stay the same for the function to return the same value of $3$ units?

 

[Jaccobtw]

It's a rightward moving wave for $v > 0$. At $t =0$, the wave takes the form of $y = f(x)$. Choose a function $f$. Something simple. For example $f(x) = x$. Draw that initial state of the wave on a graph.

Then, for $t = 1$, say, the wave takes the form $y = f(x -v) = x -v$. Draw that state of the wave on a graph. Take $v = 1$ as well, so that $y = x - 1$.

Has the wave moved left or right?

f(x) = 10 for t = 0

For t = 1, and v = 1

10-(1)(1) =9

We began at 10 and now we’re at 9, so hasn’t the wave moved to the left?