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Homework Help: Wavelength with P/Q exponent equation-solve for P/Q

  1. Jan 18, 2010 #1
    1. The problem statement, all variables and given/known data
    Speed of an ocean wave depends on the wavelength [tex]\lambda[/tex] in meters and
    gravitational field. (see equation below). Find values of P and Q. K is a constant and has no dimensions


    2. Relevant equations

    V = K[tex]\lambda[/tex]PgQ

    3. The attempt at a solution

    V=velocity, which is m/s
    and i can disregard K because it is a constant which has no dimensions.
    g = m/s2
    [tex]\lambda[/tex] = m
    plugging in the numbers; i get:

    m/s = mP(m/s2)Q

    here is where i get lost. i dont know how to bring the exponents down so i can solve for it
     
  2. jcsd
  3. Jan 18, 2010 #2

    Mark44

    Staff: Mentor

    You have V = K LPgQ
    (I used L in place of lambda.)
    So LP = V/[K gQ]

    To solve for P, take the log of both sides, then divide both sides by log L.

    To solve for the other exponent Q, first solve for gQ in a way similar to how I solved for LP, then take the log of both sides, and divide both sides by log g.
     
  4. Jan 18, 2010 #3
    are you sure? i was workin on this with my prof and he told me not to take the log; thats what i thought of doing initially
    and i have no numerical values for the equations; its all dimension analysis
     
  5. Jan 18, 2010 #4

    Mark44

    Staff: Mentor

    OK, what's the exact statement of the problem? As you have it in post 1, it appears that you need to solve for P and Q.
     
  6. Jan 18, 2010 #5
    The speed of ocean waves depend on their wavelength [tex]\Lambda[/tex] (measured in meters) and the gravitational field strength g (measured in m/s^2) in this way:

    v = [tex]\Lambda[/tex]PgQ

    where K is a dimensionless constant. Find the values of the exponents P and Q
     
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