Wave movement and particle movement

[hello478]

Homework Statement

A wave pulse moves along a stretched rope in the direction shown.
Which diagram shows the variation with time t of the displacement s of the particle P in the rope?
diagrams below

Relevant Equations

answer is D

A wave pulse moves along a stretched rope in the direction shown.

Which diagram shows the variation with time t of the displacement s of the particle P in the rope?​

A

B

C

D

my answer was c because i thought that the particle would move in the same way the wave was coming...

 

[BvU]

Draw this picture on a strip of paper

Put it under a blank sheet of paper with the P on the right sticking out a little bit.
Now slowly pull the strip to the right

Get the idea?

 

[hello478]

Draw this picture on a strip of paper
View attachment 341725

Put it under a blank sheet of paper with the P on the right sticking out a little bit.
Now slowly pull the strip to the right

Get the idea?

i did and its the same pattern as shown in c
can you please explain it theoretically?

 

[BvU]

i did and its the same pattern as shown in c
can you please explain it theoretically?

Ha, the strip shows the pattern as in C. Yes.
But if you make a plot of the vertical position of the point where the line comes out from under the blank paper --as a function of the distance over which you pulled the strip, you get D

I grant you that the P is confusing. You want to consider it as a bead on the string that does not move with the string, but stays in position.
(i.e. on the right edge of the blank paper as you move the strip to the right).

$\$

 

[hello478]

Ha, the strip shows the pattern as in C. Yes.
But if you make a plot of the vertical position of the point where the line comes out from under the blank paper --as a function of the distance over which you pulled the strip, you get D

I grant you that the P is confusing. You want to consider it as a bead on the string that does not move with the string, but stays in position.
(i.e. on the right edge of the blank paper as you move the strip to the right).

$\$

but listen
think of it like waves on a water if this is a wave, P is a duck on the water, it will cause it to move up first...
and the wave will come out as moving upwards from under the paper too

 

[hello478]

im back
thank you for your efforts

 

[BvU]

but listen
think of it like waves on a water if this is a wave, P is a duck on the water, it will cause it to move up first...
and the wave will come out as moving upwards from under the paper too

Correct! And which way is the ducks initial movement in picture C?

 

[hello478]

Correct! And which way is the ducks initial movement in picture C?

it moves upwards

 

[Hill]

it moves upwards

Looking at C:

What happens first, time "1" or time "2"?

 

[hello478]

Looking at C:
View attachment 341734
What happens first, time "1" or time "2"?

time 2 happens first

 

[Hill]

time 2 happens first

Which way the time goes on this graph, to the right or to the left?

 

[hello478]

Which way the time goes on this graph, to the right or to the left?

time is 0 at the left and increases on the right

 

[Hill]

time is 0 at the left and increases on the right

Then, which happens earlier, "1" or "2"?

 

[hello478]

Then, which happens earlier, "1" or "2"?

then 1 happens first because its time is earlier

 

[Hill]

then 1 happens first because its time is earlier

Exactly. So, on the C the point would move down first, wouldn't it?

 

[hello478]

Exactly. So, on the C the point would move down first, wouldn't it?

yeah, then?

 

[hello478]

Exactly. So, on the C the point would move down first, wouldn't it?

the answer is D, how?

 

[Hill]

yeah, then?

Then, the answer is not C, because as you correctly said about the point P,

it moves upwards

 

[hello478]

Then, the answer is not C, because as you correctly said about the point P,

ohhh i got ittt
thanks alotttt

 

[kuruman]

ohhh i got ittt

Now that you got it, do you see why the required answer is the mirror image of the given waveform about point P?

 

[hello478]

Now that you got it, do you see why the required answer is the mirror image of the given waveform about point P?

its still a bit confusing, can you explain it to me?
is it because the part of wave which is in front is produced first, it gets to hit P first so it causes it to move up

 

[kuruman]

Imagine that you are standing fixed at point P as the wave goes by you. You measure the following displacements from the baseline and times:
$y_A = -1~$cm at time $t_A.$
$y_B = +2~$cm at time $t_B.$
$y_C = +2~$cm at time $t_C.$

Order the times from earliest to latest and mark them on a time axis.
Make a plot of $y$ vs time.
Connect the dots. What do you get?

 

[haruspex]

The easiest way is to switch to the frame of reference of the pulse. So that stays still while P moves to the left. Clearly that flips the picture about a vertical axis.
The reason is that the picture is drawn with the pulse moving to the right, so going along the x axis from left to right is going backwards in time. Had the picture been the other way around the answer would have been obvious.

 

[kuruman]

$\dots$ so going along the x axis from left to right is going backwards in time.

Which is the mirror image of the given pulse.