# Displacement v Time graph for a wave

1. Feb 24, 2013

### trollcast

1. The problem statement, all variables and given/known data

I'm given a graph with displacement in metres on the y-axis and time on the x-axis. The graph represents the displace of a particle of a spring that has a mechanical wave passing through it

The graph is just a simple sine wave.

It then asks to describe the displacement of the particle compared to the velocity of the wave and then state and explain whether the wave is longitudinal or transverse.

2. Relevant equations
3. The attempt at a solution

Since the particles displacement is changing from positive to negative periodically I'm assuming the particle is oscillating in the direction of the waves velocity so therefore the wave would be longitudinal since the particle is vibrating parallel to the direction of motion of the wave?

2. Feb 24, 2013

### Simon Bridge

Well OK, but what has that to do with the task you have been set?

By "velocity of the wave", which wave do they mean? The wave of the mass oscillating that you have been given or the wave travelling along the spring? (Are you sure this is a mass moving as a result of a wave travelling along a spring and not SHM?)

3. Feb 24, 2013

### trollcast

Thats all the question states:

A wave of fixed velocity passes along a spring.
The graph below shows a graph of the displacement, d of a particle of the spring against time t.

Describe the direction of the particles displacement relative to the velocity of the wave and therefore state the type of wave and explain why you chose this:

It couldn't be SHM as we haven't covered that yet.

4. Feb 24, 2013

### Simon Bridge

Uh OK - there's not enough information is there? How would you know if the displacement on the graph is measured along the velocity of the wave or perpendicular to it?

The particles could be oscillating side-to-side as the spring lies along the floor. Displacement to the left being positive and to the right being negative.

5. Feb 24, 2013

### trollcast

The only other information you're given is a couple of numbers on the graph but they're no help?

I looked at the next page and it says its actually a string, must be a misprint on the first page, so I'm going to say transverse and just hope its right.

6. Feb 24, 2013

### Simon Bridge

Task requires a reason ... "I hope it's right" is a good enough reason?
Can strings not carry longitudinal waves?
But you have the right idea - the clue is probably in context rather than actually written down. What would be accepted as a reason? Is there anything in your course notes?

7. Feb 24, 2013

### trollcast

Ah found it now, it says the string is under a constant tension so that would stop a longitudinal wave being formed along it since the "pressure" (not sure whats the right word since its a string) difference can't be formed.

8. Feb 24, 2013

### Simon Bridge

There you go - if the tension is uniform along it's length then compressions and expansions cannot be present. When you pull a guitar string, doesn't it stretch? Can you get a transverse displacement without stretching the string?