Spring set makes up a traveling wave

[Jenny Physics]

Homework Statement

Twelve identical mass-spring combos are lined up and set to oscillation. Two pictures of the same system taken at different times are shown. The crest-to-crest distance is 8.0 cm, and the maximum displacement of all the masses is 1.5 cm.

1) Explain how you can tell that a traveling wave is present.

2) Which direction is the wave traveling? Be sure to justify your response with a reasoned explanation.

3) Make an estimate of the period of oscillation of each mass.

4) What is the frequency of the traveling wave?

5) What are the amplitude and the wavelength of the traveling wave?

6) What is the wave speed?

Homework Equations

wave velocity = lambda * frequency

The Attempt at a Solution

1) The synchronized motion of the springs up and down causes a transverse wave to propagate with some period, amplitude and frequency?2) To the right by looking at the two consecutive images?

3) The amplitude of the motion is given but not the k or m so we can't use the usual formula for the period. We must use information about the wave to figure out the period of each spring.

4) We know the wavelength (8 cm) but don't know the speed of the wave, so not sure how to find the frequency.

5) The amplitude is probably 1.5 cm? (the max displacement of a mass)? The wavelength is 8cm?

6) The wave speed will be wavelength * frequency so if I could solve the previous questions this one would be easy to answer.

 

[BvU]

1) But there isn't ! There is no coupling of the motions

 

[kuruman]

1) The synchronized motion of the springs up and down causes a transverse wave to propagate with some period, amplitude and frequency?

Close enough.

2) To the right by looking at the two consecutive images?

Explain this better. What do you see when you look at the two consecutive images that makes you conclude "to the right"?

3) The amplitude of the motion is given but not the k or m so we can't use the usual formula for the period. We must use information about the wave to figure out the period of each spring.

Look at the two consecutive pictures, carefully this time and concentrate on a peak. How much time do you think must elapse for this peak to travel the distance of one wavelength?

This should get you started in the right direction

 

[Jenny Physics]

Look at the two consecutive pictures, carefully this time and concentrate on a peak. How much time do you think must elapse for this peak to travel the distance of one wavelength?

This should get you started in the right direction

Not sure. Looking at the two images I can see that the leftmost spring moved up and the middle ones appear not to have moved. After one period the two peak springs will probably be fully stretched? But what does that tell me?

 

[kuruman]

What is the distance between to adjacent masses?
Concentrate on one mass, say mass 2 at t = 0.15 s. How much time does it need to get to the vertical position that mass 3 has at t = 0.15 s?

 

[Jenny Physics]

What is the distance between to adjacent masses?
Concentrate on one mass, say mass 2 at t = 0.15 s. How much time does it need to get to the vertical position that mass 3 has at t = 0.15 s?

The distance between spring 4 and spring 12 is 8 cm, which comes to 1 cm between springs. At time t=0.15 spring 2 seems to be in equilibrium with gravity. I imagine you mean there is a relation between the wavelength of the wave and the period of the springs but I just don't see it.

 

[haruspex]

The synchronized motion of the springs up and down causes a transverse wave to propagate with some period, amplitude and frequency?

I'm afraid that doesn't do it. Your answer must involve comparing the images. If we only look at one image, it could be a standing wave. I.e., all masses above the red line are descending, all those below are ascending, and those on the red line are stationary.

Looking at the two images I can see that the leftmost spring moved up and the middle ones appear not to have moved.

No, they have all moved.
This is a trick question. Have you ever watched a movie and seen car wheels apparently rotating the wrong way?

The distance between spring 4 and spring 12 is 8 cm, which comes to 1 cm between springs. At time t=0.15 spring 2 seems to be in equilibrium with gravity. I imagine you mean there is a relation between the wavelength of the wave and the period of the springs but I just don't see it.

No, the horizontal separation of the springs is not of interest here. Kuruman is asking you to compare the vertical positions.
But I would have chosen the leftmost two masses. In the first picture, the second mass is on the red line. How long does it take for the first mass to reach the red line (setting aside the trick question for now)? So how long does it take the first mass to reach the position of the third mass in the first picture? Etc?

 

[Jenny Physics]

I'm afraid that doesn't do it. Your answer must involve comparing the images. If we only look at one image, it could be a standing wave. I.e., all masses above the red line are descending, all those below are ascending, and those on the red line are stationary.

No, they have all moved.
This is a trick question. Have you ever watched a movie and seen car wheels apparently rotating the wrong way?

No, the horizontal separation of the springs is not of interest here. Kuruman is asking you to compare the vertical positions.
But I would have chosen the leftmost two masses. In the first picture, the second mass is on the red line. How long does it take for the first mass to reach the red line (setting aside the trick question for now)? So how long does it take the first mass to reach the position of the third mass in the first picture? Etc?

I can't tell because I don't know if the first spring is fully stretched and what is the relative distance between the 1st and 3rd etc. I know that the 4th string is probably fully compressed and the 8th is probably fully stretched so the distance from the max to the minimum is probably 2* 1.5 cm?

 

[haruspex]

I can't tell because I don't know if the first spring is fully stretched and what is the relative distance between the 1st and 3rd etc.

I assume that is in reply to this question:

In the first picture, the second mass is on the red line. How long does it take for the first mass to reach the red line

I did not ask about distance, I asked about time.
In the first picture, the first mass is below the red line and the second mass is on it. In the second picture (taken how much later?) the first mass is on the red line. The second mass, meanwhile, has moved to where the third mass had been.
If you were take a third picture, later again by the same time interval, where would the first mass be?

 

[Jenny Physics]

I assume that is in reply to this question:

I did not ask about distance, I asked about time.
In the first picture, the first mass is below the red line and the second mass is on it. In the second picture (taken how much later?) the first mass is on the red line. The second mass, meanwhile, has moved to where the third mass had been.
If you were take a third picture, later again by the same time interval, where would the first mass be?

It takes the first mass 0.03 secs to reach the top (max compression) i.e. spring 4 position at t=0.15secs. It takes another 0.08 secs to reach the max again (the position of the last spring) so the period of each spring must be 0.08 secs?

 

[haruspex]

It takes the first mass 0.03 secs to reach the top (max compression) i.e. spring 4 position at t=0.15secs. It takes another 0.08 secs to reach the max again (the position of the last spring) so the period of each spring must be 0.08 secs?

Yes, that is a valid value for the period. There are other possible periods, but we'll address that later.
Do you have any response to my challenges to your answers to 1 and 2?

 

[Jenny Physics]

Yes, that is a valid value for the period. There are other possible periods, but we'll address that later.
Do you have any response to my challenges to your answers to 1 and 2?

For 1 and based on 3, the idea must be that for t less than a period the springs trace a sinusoid and because the springs motion is oscillatory that sinusoid will repeat.
For 2 I assume from your suggestion that the wave must be traveling to the right but not sure why

 

[haruspex]

because the springs motion is oscillatory that sinusoid will repeat.

Reread my comment. A standing wave will also exhibit a sinusoid, repeatedly. You have to use the differences between the two images to show that it is a traveling wave.

I assume from your suggestion that the wave must be traveling to the right

Not that it must be, but that it could be. There is not enough information to be sure.
Suppose it is traveling to the right. What would you now calculate for the period?

 

[Jenny Physics]

Not that it must be, but that it could be. There is not enough information to be sure.
Suppose it is traveling to the right. What would you now calculate for the period?

0.08 secs since it is the time it takes for second mass to do a full oscillation

 

[haruspex]

0.08 secs since it is the time it takes for second mass to do a full oscillation

As I mentioned, 0.08s is only one possibility.
Consider this: what would the second picture look like if it had been taken 0.07s after the first one, i.e. after just less than one period? Given only that picture and the first one as is, which way would you think the wave is moving?

 

[kuruman]

Perhaps a few additional thoughts will help you see what is going on and what haruspex is hinting at.
Look at mass 1 and imagine what it could be doing from 0.15 s to 0.16 s. Here are some possibilities
1. At 0.15 s it is moving up and reaches y = 0 at 0.16 s, still moving up.
2. At 0.15 s it is moving up, crosses zero, comes back down and at 0.16 s it is at y = 0 moving down.
3. At 0.15 s it is moving down, reaches maximum displacement in the negative direction, and at 0.16 s it crosses zero for the first time.

One can go on like this and devise different scenarios, adding any number of half periods to the time interval between 0.15 and 0.16 s. The direction of propagation and speed of the wave depend on the scenario. This ambiguity of snapshot interpretation is known as temporal aliasing, sometimes called the wagon wheel effect. My own sense is that the creator of the question had scenario 1 (the simplest interpretation) in mind but did not formulate the question in a way that would exclude the other possibilities.

 

[haruspex]

My own sense is that the creator of the question had scenario 1 (the simplest interpretation) in mind but did not formulate the question in a way that would exclude the other possibilities.

Possibly, but note this admonition in 2):

Be sure to justify your response with a reasoned explanation.

It is not possible to justify the answer without considering the possibility of the other solutions.