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Another Simple Physics Problem

  1. Jan 8, 2012 #1
    1. The problem statement, all variables and given/known data

    Two steel wires are stretched with the same tension. The first wire has a diameter of .00059 meters and the second wire has a diameter of .00089m. If the speed of waves traveling along the first wire is 54.0 m/s, what is the speed of the waves along the second wire?

    2. Relevant equations

    v=√Ft/μ
    μ=m/L


    3. The attempt at a solution

    I have no idea how to get the mass or length of the string...
     
  2. jcsd
  3. Jan 8, 2012 #2
    Hint: You know the diameters so you know the mass per unit length of each.
     
  4. Jan 8, 2012 #3
    what would be the equation for that... i only know μ=m/L...
     
  5. Jan 8, 2012 #4
    You know the formula for velocity. The tension is the same for both wires. Mu is mass per unit length which you can determine by realizing that a wire is a cylinder. You know the velocity of the wave on one of the wires. Therefore, you can solve this without knowing the respective wire lengths.
     
  6. Jan 8, 2012 #5
    imdont have e height though... how can you convert the diameter into something usable...
     
  7. Jan 8, 2012 #6
    m/l is mass per unit length.
     
  8. Jan 8, 2012 #7
    What's the formula for the volume of a cylinder?
     
  9. Jan 8, 2012 #8
    pi r^2h
     
  10. Jan 8, 2012 #9
    That's correct or you could also say (pi d^2/4)h. So what would be the mass per unit length?
     
  11. Jan 8, 2012 #10
    radical x over 54^2?
    x being the tension?..
     
  12. Jan 8, 2012 #11
    Do you know what mass per unit length means?
     
  13. Jan 8, 2012 #12
    linear density
     
  14. Jan 8, 2012 #13
    In the case of a wire which is a cylinder the mass per unit length is:

    m/L = rho * Volume/L = rho * pi * d^2/4 * L/L = rho * pi * d^2/4

    where rho is the density in kg/meter^3.

    You have the formula for the velocity of one wave at a specific m/L. You want the velocity of the wave in the other wire. The tensions are the same.

    V1^2 = F/mu1 and V2^2 = F/mu2. Think about (V1/V2)^2.
     
  15. Jan 8, 2012 #14
    Got to hurry here. Giants-Falcons game starts in 11 minutes!
     
  16. Jan 8, 2012 #15
    how do you find the density or linear density? this is crazy
     
  17. Jan 8, 2012 #16
    You do not the actual number; you only need the ratio of the two.

    V1^2 = F/mu1 and V2^2 = F/mu2. Think about (V1/V2)^2.
     
  18. Jan 8, 2012 #17
    idk....
     
  19. Jan 8, 2012 #18
    D
    What is idk?
     
  20. Jan 8, 2012 #19
    i dont know.
     
  21. Jan 8, 2012 #20
    Ok, I shall provide more help. I cannot do it for you -forum rules.

    Form a ratio for v1/v2. You know one of the v's. This ratio equals square root of mass per unit length ratios. You can compute this ratio. This leaves one unknown.
     
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