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Wave Speed As a Function of Tension

  1. Oct 4, 2007 #1
    1. The problem statement, all variables and given/known data
    This is a question from my lab manual
    v=Cmu^aT^b (4.3)
    Use dimensional analysis of equation (4.3) to determine the exponents a and b.

    2. Relevant equations
    i know that the proper equation is
    v=sqrt(T/mu)


    3. The attempt at a solution
    I tried dimensional to get some sort of exponent of 1/2 and -1 for mu in there...but not much luck. can anyone tell me what i'm doing wrong?

    m/s = (kg/m)(kgm/s^2)
    m/s = kg^2/s^2
    ms = kg^2
    sry...i've always been bad at dimensional analysis x_x any help would be greatly appreciated!!
     
  2. jcsd
  3. Oct 4, 2007 #2

    learningphysics

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    What is mu?
     
  4. Oct 4, 2007 #3
    sry forgot to say
    mu is mass per unit length of the wire
     
  5. Oct 4, 2007 #4

    learningphysics

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    okay, so

    m/s = (kg/m)^a* (kgm/s^2)^b

    and simplifying this:

    m/s = kg^(a+b)*m^(b-a)*s^(-2b)

    now using the exponents of kg, m and s on both sides... try to get some equations and solve for a and b.
     
  6. Oct 4, 2007 #5
    by using exponents on both side, do u mean to raise m/s to the power of (a+b)(b-a)(-2b)??
     
  7. Oct 4, 2007 #6

    learningphysics

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    no. you need the exponents to match on both sides...

    what is the exponent of kg on the left side? what is the exponent of kg on the right side?
     
  8. Oct 4, 2007 #7
    now i get it! thanks so much!

    the ansr i got was a=-1/2 and b=1/2, which is in accordance with
    v = sqrt(T/mu)
     
    Last edited: Oct 4, 2007
  9. Oct 4, 2007 #8

    learningphysics

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    yup. Looks good!
     
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