1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Dimensional analysis to determine unknown exponents

  1. Oct 25, 2008 #1
    1. The problem statement, all variables and given/known data
    1. Use the method of Dimensional Analysis to show that the unknown exponents in Equation (1) are l=-1/2, m=-1, and n=1/2.

    2. Relevant equations
    Equation (1) is [tex]\lambda = k \mu ^{l} f ^{m} T^{n}[/tex]

    Where:
    [tex]\lambda[/tex] is the wavelength;
    f is the frequency of the sound;
    T is the tension in the string;
    [tex]\mu[/tex] is the mass per unit length of the string.
    k is a dimensionless constant.

    3. The attempt at a solution
    The dimensions for the above terms should be:
    [tex]\lambda = [L][/tex] (Simple enough)
    [tex]f=[L] ^{-1}[/tex] (Since the frequency is the inverse of time. Is this correct?)
    [tex]T=[M][L][T] ^{-2}[/tex] (Since the tension in the rope is just the force exerted on it, right?)
    [tex]\mu = [M][L] ^{-1}[/tex] (Since it is the mass per unit length)

    Which gives the dimensional equation as:
    [tex][L]=([M] \cdot [L]^{-1}) ^{l} \cdot ([T] ^{-1}) ^{m} \cdot ([M] \cdot [L] \cdot [T]^{-2})^{n}[/tex]

    Which can be used to make equations for [L], [T], and [M], respectively:

    1=-1l + 1n ([L]) (i)
    0=-1m - 2n ([T]) (ii)
    0=1l + 1n ([M]) (iii)

    And from here I don't know where to go. If I manipulate (ii) to state n in terms of m, I get n=-1/2m. But where do I go from here? I need to solve these three equations simultaneously?
     
    Last edited: Oct 25, 2008
  2. jcsd
  3. Oct 25, 2008 #2
    Oh, I got it. Sorry, I keep doing this with my posts here. XD
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Dimensional analysis to determine unknown exponents
  1. Dimensional analysis (Replies: 4)

  2. Dimensional Analysis (Replies: 5)

  3. Dimensional Analysis (Replies: 1)

  4. Dimensional analysis (Replies: 3)

Loading...