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Answer Checking (Speed of Sound formula, dimensional analysis)

  1. Sep 23, 2012 #1
    1. The problem statement, all variables and given/known data
    One formula for measuring the speed of sound in air is:
    [itex]
    v=\sqrt\frac{kTg}{m}
    [/itex]

    v=velocity
    T=temperature
    g=dimensionless constant
    m=average mass of an air molecule

    If all units are SI, what are the units of k?


    3. The attempt at a solution

    I've done a lot of Googling to first try and find formulas for the speed of sound. The most similar I've seen on Wikipedia was
    cc8e66050f6b9537574f750498ec6eb1.png
    with the last part of the formula being the most relevant
    Cideal = ideal speed
    gamma = adiabatic index
    k = Boltzmann Constant
    T = temperature in Kelvin
    m = mass of a single molecule in kg

    That makes me think that k is a placeholder for the adiabatic index or the Boltzmann Constant, but I'm not sure which (if either) it is.

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

    In this question, the length of a wave, λ, has dimensions L, wave speed (v) has dimensons L/T, and gravitational acceleration (g) has units of L/T². Could the following be an equation for wave speed:

    2. Relevant equations

    [itex]
    v=\sqrt\frac{g}{λ}
    [/itex]

    3. The attempt at a solution
    λ=L
    v=D/T
    g=L/T²

    [itex]
    D/T = \sqrt\frac{L/T²}{L}
    [/itex]

    [itex]
    D/T=\sqrt{T²}
    [/itex]

    [itex]
    D/T=T
    [/itex]

    No it could not be an equation for wave speed because it is not dimensionally proportionate.

    If I didn't get these right, where did I go wrong? I feel like I got the second one right, but I'm completely clueless on the first one. Thanks in advance!
     
    Last edited: Sep 23, 2012
  2. jcsd
  3. Sep 23, 2012 #2

    rock.freak667

    User Avatar
    Homework Helper

    No need to look for similar equations. They just wanted you to get the units of k.

    you have velocity on the left side in m/s. Write down the units of the rest of units of the dimensions. Then put them into the formula and re-arrange to find k.

    This one is correct.
     
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