How can I understand wave graph conversion better?

[riceking95]

Homework Statement

Number 6:

For this problem I'm changing the wave speed to 3.0 m/s instead of 1 m/s because that's what our teacher instructed us to do.

Homework Equations

None that I know of

The Attempt at a Solution

I'm having the hardest time making connections between the graphs and more specifically converting one graph to the other. I understand that the snapshot graph represents the displacement of the wave as a function of x and make the analogy of "the experience" a particle will go through. Also I know that the history graph shows what is happening to the medium at the specific point. But when it comes to graphs that are a bit more complex than easier x positions and different velocities I lose track of what's going on.

With this problem it says it is a history graph at x=2m with the wave moving at 3 m/s. Knowing this I would say that for the snapshot, the 2m will be affected immediately by the wave because of the placement of the leading edge on the history graph.
I also recognized from my teacher's solution that each second that's hashed on the graph is equivalent to the 3 meters which is understandable, but I really can't connect with what's going on overall. Any help would be greatly appreciated, thank you.Here's my teacher's solution:

 

[BvU]

Hello Riceking,

Well, you got most of it!
From the figure in the book you saw x=2 starts going up at t=0 and is back to 0 at t=4, so the whole snapshot "up from zero" width must be 12 m.
Similarly: x=2 is at its peak at t=1, so the rising flank of the wave is 3 m wide. With the 1 cm amplitude, that's enough to draw teacher's picture.
Change from 1 m/s to 3 m/s was probably introduced by teacher becasue 1 m/s is almost too easy (either that, or he doesn't want to see tiny drawings being handed in )

My advice: practice.
What worked very well for me: drawing waves on transparencies and move them sideways over a piece of paper with coordinate lines.

 

[riceking95]

Hello Riceking,

Well, you got most of it!
From the figure in the book you saw x=2 starts going up at t=0 and is back to 0 at t=4, so the whole snapshot "up from zero" width must be 12 m.
Similarly: x=2 is at its peak at t=1, so the rising flank of the wave is 3 m wide. With the 1 cm amplitude, that's enough to draw teacher's picture.
Change from 1 m/s to 3 m/s was probably introduced by teacher becasue 1 m/s is almost too easy (either that, or he doesn't want to see tiny drawings being handed in )

My advice: practice.
What worked very well for me: drawing waves on transparencies and move them sideways over a piece of paper with coordinate lines.

Hi BvU thank you for replying. Your explanation makes much more sense than I could understand by myself. Now, after what you said, I infer we use the snapshot graph to dictate what happens to the history graph after moving the position of the snapshot graph back to t=0sec? And for looking at the history graph and drawing the snapshot (like in problem 7), we would move the graph vt = x amount?