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Tension and waves help

  1. Nov 13, 2007 #1

    sun

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    1. The problem statement, all variables and given/known data

    A circus performer stretches a tightrope between two towers. He strikes one end of the rope and sends a wave along it toward the other tower. He notes that it takes the wave 0.880 s to reach the opposite tower, 20.0 m away. If a 1 meter length of the rope has a mass of 0.255 kg, find the tension in the tightrope.


    2. Relevant equations

    v-f(lambda)
    v=sqrt.(tension/mu)
    mu=mass per unit length
    tension=mg
    f=1/t

    3. The attempt at a solution

    I solved for wave speed using v=f(lambda)
    f=1/T=1/.88s=1.136Hz
    Delta(x)=lambda=20m, so 20m x 1.136=22.72m/s

    Tension=v^2(mu) = (22.72)^2(.225/20) or (22.72)^2(.225/1) ??

    I'm not sure what i'm doing wrong. Suggestions would be appreciated.

    thanks
     
    Last edited: Nov 13, 2007
  2. jcsd
  3. Nov 13, 2007 #2

    Doc Al

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    Staff: Mentor

    I'm not following all that calculation. You are not given any data about f, T, or lambda.

    The speed can be found simply by v = d/t = 20/.88 = 22.72m/s.

    .225 kg is the mass of a 1 m section; so mu = mass/length = .225 kg/m.
     
  4. Nov 13, 2007 #3

    sun

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    i don't know what i'm doing wrong when i use 22.72 to calculate the tension in the rope using: v=sqrt.(tension/mu)

    maybe i'm calculating mu incorrectly? any ideas?

    thank you very much
     
  5. Nov 13, 2007 #4

    Doc Al

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    Staff: Mentor

    You used two versions of mu. One is right; one is wrong.
     
  6. Nov 13, 2007 #5

    sun

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    from what i've read i believe mu=.225 is the correct one. Because that is the mass for every 1 meter of string. Regardless of the mu i've been using i still get an incorrect answer.

    this is why i'm still a bit confused.

    thank you
     
  7. Nov 13, 2007 #6

    sun

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    suggestions as to what i may be doing wrong would be greatly appreciated.
     
  8. Nov 13, 2007 #7

    sun

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    i get 116.15N when i solve for tension, but this is wrong.

    I could really use some help as soon as possible, please.

    thank you
     
  9. Nov 14, 2007 #8

    Doc Al

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    Staff: Mentor

    typo!

    Here's the likely problem: In your first post you state the mass as 0.255 kg, but in later posts you use 0.225 kg. Recalculate the answer using the correct value.
     
  10. Nov 14, 2007 #9

    sun

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    Pure Genius!! :P

    At the rate i was going, i definitely would not have noticed that. :(

    thank you
     
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