How to interpret a displacement-position graph? I have a good understanding of Displacement-time graphs and position-time graphs and how to interpret them. I take the IB diploma and came across this question from a 2009 paper with a displacement-position graph but our textbook does not help interpret it and neither can I find an internet article with explanations
Here is the question. So the answer is C meaning the velocity is downwards. But I thought the particle starts at its mean position, travels to the left and back to the mean position, and then begins travelling to the right. So at point P the particle should be moving in the right direction. The question says at the wave travels left to right so how can the velocity really be downwards?

 A: The overall wave shown is traveling to the right. The individual particles in a transverse wave do not move to the left and right (parallel to the direction of the wave). They move up and down (transverse to the wave direction). What you see as a "wave" is really just the procession of particles moving up and down in sequence as if they were on little springs. They are moving in a direction transverse to the direction of the wave!
You can simulate the effect with a bedsheet that's tucked in on both sides. Place a small object on the sheet and then slide your hand underneath it. You can consider the direction you slide your hand to be the wave's direction. You'll notice as your hand approaches it, the particle itself doesn't move in the same direction as your hand, it moves up. As your hand passes underneath it, the particle begins moving back down (this is where the particle in your diagram is).
If the wave were a longitudinal wave (a compression wave like sound waves and waves down a slinky when you give it a push along the length of the spring) then the individual particles would move parallel with the wave direction (the individual particles still stay close to their original position, only the wave travels).
In fact, whether a particle moves perpendicularly or parallel to the wave's direction is what defines whether a wave is transverse or longitudinal.
A: The particle does not travel left-right. It is a transversal wave traveling left-right. This means that the particles are moving either up-down or forward-backward (perpendicular to the page). None of the particles in the wave are mving-left-right.
Here they don't consider the direction perpendicular to the page so the only direction to consider is up-down
To see if it's up or down just draw the same graph for a little later time. You know that it propagates to the right so it will be shifted to the right. Then look at the displacement of the same particles on the two graphs.
A: Since the wave is an transverse wave the particles will move perpendicular to the direction of propagation so we can eliminate B,D
Now we know that the velocity of any particle is given by $v_{Particle}=-v_{wave}*\text{(Slope of the graph at particle)}$
Proof: Let equation of wave be $y=A\;sin(wt-kx+a)$ then velocity of particle is: $\frac{dy}{dt} = v_{particle}=A \omega \; cos(wt-kx)$ ①
Slope of graph is: $dy/dx= m =- Ak \; cos(wt-kx+a)$ ②
From equation ①,②: $v_{particle}=-\omega/k*m=-v_{wave}*m$ (Since velocity of wave is given by $\frac{w}{k}$)
As per the given question wave travels from left to right ie v(w)= positive and the slope of graph at given particle location is also positive So if we apply this, $-(\text{positive }v_{wave})(\text{positive slope})=\text{negative }v_{particle}$, so it moves downward (c is your answer)
