Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

General equation for the speed of sound?

  1. Feb 5, 2012 #1
    I've seen stated in many a physics book that the general case for the speed of sound (for general equations of state p(ρ) ) is given by

    [tex] c^2 = \frac{\partial p}{\partial \rho} [/tex]

    where p is pressure and ρ is density.

    but I can't for the life of me figure out how on earth to derive that. I've seen tons of derivations for specific cases--gasses, solids, but not for the general case. According to wikipedia, it can be derived using classical mechanics. Can someone point me in the right direction?
    Last edited: Feb 5, 2012
  2. jcsd
  3. Feb 22, 2012 #2
    c = [itex]\sqrt{P/\rho}[/itex]

    Where P = coefficient of "stiffness"
    and [itex]\rho[/itex] = density
  4. Feb 22, 2012 #3
    oops sorry. Didn't understand your initial question. I just jumped to conclusions.
  5. Jan 14, 2013 #4
    the equation of state is p=p(ρ,s) thus

    dp = ([itex]\frac{∂p}{∂\rho}[/itex][itex])_{s}[/itex]d[itex]\rho[/itex] + ([itex]\frac{∂p}{∂s}[/itex])[itex]_{\rho}[/itex] ds

    I am guessing that because ([itex]\frac{∂p}{∂\rho}[/itex][itex])_{s}[/itex] has units of "velocity squared", it is looked upon as such;
    But why this velocity is the sonic one - beats me...

  6. Jan 14, 2013 #5
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook