Answering the Rope Tension & Frequency Questions

[kolua]

Homework Statement

Identical ropes were tied to two trees, and two men, A and B, started shaking the free ends at the same instant a short while ago (Figure 1) .

Which rope has the greater tension?
Which man is shaking with the greater frequency?

Homework Equations

T=1/f λf=v

The Attempt at a Solution

For the first question, I would like to go for that rope B has greater tension, because the whole rope is moving.
For the second question, I went for A>B, because the wavelength is shorter in A than in B. But the answer is wrong, should I go for B>A then? Because the tension in B may be larger than A?

 

[Dr. Courtney]

You need the relationship between tension and frequency.

 

[kolua]

You need the relationship between tension and frequency.

the greater the tension the greater the frequency

 

[TSny]

At the time shown, how many times has person A moved the rope up and down since the start?

 

[kolua]

At the time shown, how many times has person A moved the rope up and down since the start?

this information is not given in the question

 

[TSny]

Can you deduce it from the figure?

 

[kolua]

Can you deduce it from the figure?

5 times?

 

[kolua]

Can you deduce it from the figure?

does this mean that B has higher frequency because he moved 6 times up and down for the same time interval? thus the tension in b is also greater.

 

[TSny]

OK, roughly 5 (it's hard to tell exactly). How about B?

 

[kolua]

OK, roughly 5 (it's hard to tell exactly). How about B?

6

 

[TSny]

does this mean that B has higher frequency because he moved 6 times up and down for the same time interval?

Sounds right to me.

thus the tension in b is also greater.

The frequency is not directly related to the tension. If you put a certain tension in the rope, you can wiggle it at a high frequency or a low frequency (for the same tension). So, in that sense, the frequency is independent of the tension. Higher frequency does not necessarily imply higher (or lower) tension.

 

[kolua]

Sounds right to me.
The frequency is not directly related to the tension. If you put a certain tension in the rope, you can wiggle it at a high frequency or a low frequency (for the same tension). So, in that sense, the frequency is independent of the tension. Higher frequency does not necessarily imply higher (or lower) tension.

so the tension would be equal if the rope is the same

 

[TSny]

so the tension would be equal if the rope is the same

The tension depends on how hard the person pulls horizontally on the rope.

 

[kolua]

The tension depends on how hard the person pulls horizontally on the rope.

A>B? because part of the string is undisturbed.

 

[TSny]

What do you mean when you write A>B?

 

[kolua]

What do you mean when you write A>B?

tension of string A is greater than that of B

 

[TSny]

Have you learned any relationship between tension and wave speed?

 

[kolua]

Have you learned any relationship between tension and wave speed?

the greater the tension the greater the wave speed

 

[TSny]

Yes. Try to use that to figure out which rope is under greater tension.

 

[kolua]

Yes. Try to use that to figure out which rope is under greater tension.

since wave speed equals to wave length times wave frequency. Tension of A is smaller because it has lower frequency and shorter wavelength.

 

[TSny]

since wave speed equals to wave length times wave frequency. Tension of A is smaller because it has lower frequency and shorter wavelength.

OK. That's a good argument.

Another approach: Can you tell directly from the figure which wave has the greater speed? (You might have already noticed this in your first post where you said that for B "the whole rope is moving".)

 

[kolua]

OK. That's a good argument.

Another approach: Can you tell directly from the figure which wave has the greater speed? (You might have already noticed this in your first post where you said that for B "the whole rope is moving".)

So the wave speed in B is greater because it reaches the end faster.

 

[TSny]

So the wave speed in B is greater because it reaches the end faster.

Yes.

 

[kolua]

Yes.

Thanks!