# Wave displacement on a string

1. May 28, 2013

### 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.
[Broken]
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 :)

Last edited by a moderator: May 6, 2017
2. May 28, 2013

### Staff: Mentor

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.

3. May 30, 2013

### PhyzX

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

4. May 30, 2013

### Staff: Mentor

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?

5. May 30, 2013

### PhyzX

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.

6. May 30, 2013

### Staff: Mentor

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?