Solving the Slinky Wave Problem: HELP!

[andkand97]

Homework Statement

A slinky with natural length of 3.00 meters, mass of 0.750 kg, and spring constant 18.0 N/m is stretched out along a floor, each end held by a seated person. The final length is 8.2 m. One end is plucked sending a transverse pulse. Find the pulse's travel time there AND back.

Homework Equations

I've been stuck on this problem for hours. It is driving me insane. I don't understand how to find the speed if I don't know the amplitude. Is it the natural length of 3 meters? Even then I still get the wrong answer.

The Attempt at a Solution

I've tried finding the solution multiple ways but still don't get the right answer. One method was using k = F_tension/x (8.2 m). Then putting that into v=squared root of F/(mass/length). Then used the velocity = wavelength * frequency to solve for frequency, took the inverse and multiplied by two.
PLEASE HELP! I've been working on this for hours! I'd really appreciate it.

 

[haruspex]

The find length is 8.2 m

What is that supposed to say?

k = F_tension/x (8.2 m). Then putting that into v=squared root of F/(mass/length)

That looks right, except I'm not sure that 8.2m is the right length to be using. Depends on your answer to my first question.

 

[andkand97]

What is that supposed to say?

That looks right, except I'm not sure that 8.2m is the right length to be using. Depends on your answer to my first question.

Oh sorry. It's supposed to say the final length is 8.2 meters. As in the slinky is stretched to 8.2 m.
Sorry about that.

 

[haruspex]

Oh sorry. It's supposed to say the final length is 8.2 meters. As in the slinky is stretched to 8.2 m.
Sorry about that.

OK, so how are you calculating the tension?

 

[andkand97]

OK, so how are you calculating the tension?

Well I have the spring constant and I have the distance it is stretched (8.2 m) so I do 18N/m = F/8.2m and solve for F. Is this not right? Or am I supposed to use the natural length instead?

 

[haruspex]

the distance it is stretched (8.2 m)

That's not the distance it is stretched (by).

 

[andkand97]

Oh...crap. So I subtract the natural length of 3 m from that then use it to find the tension, right?

 

[haruspex]

Oh...crap. So I subtract the natural length of 3 m from that then use it to find the tension, right?

Yes. (But I think what you did gives the speed for ;longitudinal waves.)

 

[andkand97]

How would I find the speed of a transverse wave?

 

[haruspex]

How would I find the speed of a transverse wave?

Sorry, I've confused you. I mean that using the extension (8.2-3) gives the transverse wave speed, but using the total length (as you did initially) gives the longitudinal speed.

 

[andkand97]

Oh okay. I finally got the right answer! Thank you so much I've been working on this since yesterday. Really appreciate it!