What is the displacement of a wave on a string at a given instant of time?

[ZanyCat]

"This figure is a snapshot graph of the instantaneous velocity of the particles on a string. The wave is moving to the left at 50 cm/s.

Draw a snapshot graph of the string's displacement at this instant of time."

So it seems to be a quite basic question, where it's pretty much just an integration with working out the displacement from the velocity graph.
However I don't know how to account for the 50cm/s, and if it's even relevant at all.

I've tried considering v=λf, v=ω/k, and v=-ωA*cos(kx+ωt+θ) (plus ωt because moving to the left) but have gotten nowhere, especially because I don't know how to work out the phase constant θ, and once again don't know whether it's relevant or not.

Help would be muchly appreciated :)

 

[mfb]

50cm/s gives you a reference how long a point was in those velocity regions - you need this duration for the displacement. Integrating a velocity over a length (as a direct integration would do) does not give a length.

 

[PhyzX]

I'm stuck on this question too. Can you explain exactly how you use the 50cm/s as a reference? thanks

 

[mfb]

Consider x=8cm. What is its current velocity? What was its velocity before that? When did the velocity change? How far did it move in that time frame?

 

[PhyzX]

Consider x=8cm. What is its current velocity? What was its velocity before that? When did the velocity change? How far did it move in that time frame?

Maybe I'm confused at the definition of a snapshot graph. My understanding is that each point on the graph represents a particle's vertical velocity (since waves on a string are transverse) at that position taken at one instance of time. I'm confused on how I would calculate the displacement that corresponds to each point on the velocity graph.

 

[mfb]

I'm confused on how I would calculate the displacement that corresponds to each point on the velocity graph.

Did you try to follow my steps?

Here are two more intermediate step:
What is its current velocity? What was its velocity before that? How far does the wave travel in 1 millisecond? How did the velocity graph look like 1 millisecond before? When did the velocity change? How far did it move in that time frame?