Correct statement about transverse wave propagating along a string

[songoku]

Homework Statement

Please see below

Relevant Equations

None

My answer is (1) only but my teacher said (3) is also correct. I don't understand why, I think when the wave is moving to the left both Q and R will be moving upwards, no?

Thanks

 

[hmmm27]

My answer is (1) only but my teacher said (3) is also correct. I don't understand why, I think when the wave is moving to the left both Q and R will be moving upwards, no?

Seems that way to me : you could ask them to expand on their response, see if they have the right particles.

 

[planck999]

Only 2 is correct. 1)Since P is moving downward the wave is going to right as p approaches to right. 2)Yes, since R has a longer way to go. 3) Both are going to right.

 

[haruspex]

p approaches to right.

??
P is not moving left or right, just straight down, and the wave is moving left.

Q and R will be moving upwards

Yes.

 

[kuruman]

3) Both are going to right

How do you mean that? This is a transverse wave and the points on the string can only move up and down.

 

[Orodruin]

Only 2 is correct. 1)Since P is moving downward the wave is going to right as p approaches to right. 2)Yes, since R has a longer way to go. 3) Both are going to right.

No. Each point on the string is moving up or down only. For P to be moving down, you need to find the displacement direction of the wave for which the wave at P is lower in the next instant. This occurs when the wave moves left.

2) No. The wave will have passed S completely first and the statement is false.

3) Is false regardless of direction of wave motion.

Please do not confuse students if you are not 100% certain of the answer.

 

[songoku]

Thank you very much hmmm27, Planck999, haruspex, kuruman, Orodruin

 

[Orodruin]

For P to be moving down, you need to find the displacement direction of the wave for which the wave at P is lower in the next instant. This occurs when the wave moves left.

To put that in slightly more mathematical terms:

A wave moving left/right is given by the displacement $u(x,t) = f(x \pm ct)$ (with upper sign for a wave moving left). At a given point $x = x_0$, the up/down motion of the string is given by $u_t(x_0,t) = \pm c f'(x_0 \pm ct) = \pm c u_x(x_0,t)$. The string is moving down at $x_0$ if this is negative. Since the x-derivative at P is negative, we need the positive sign for the full expression to be negative, i.e., the wave is moving left.