1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Help - Missing Step - Gas in a Tube

  1. Feb 22, 2004 #1
    Help ASAP --- Missing Step --- Gas in a Tube

    I am dealing with finding normal modes of oscillations in a continuum

    I have no problems with the string example, but now I have a gas in a tube, one side of the gas has pressure= p_0 and the other side p_0+delta p, they're separated by a wall that is lifted at t=0. This is a tube closed in the extremes.

    So, I've started with the classic wave equation for the tube
    rho is the density, P is the pressure, psi the movement
    (second partial derivatire of psi on t = second partial derivative of psi on x, times - rho_0 )and proposing the typical solution psi(x, t)= A cos(kx)cos(omega*t+phi). I also know the relationship between the speed of sound and pressure and density, and the value of delta rho.

    I start with the boundary conditions to solve for k, and now it is time to write out the initial conditions, and from there solve for A and phi. According to the string example, one of these conditions will end up as a function f(x) to be solved by Fourier.

    The problem is, I can't see for the life of me which are the initial conditions in a gas! And I can't see what kind of function it would be either. In a string I just see where the string is at time=0 and what velocity it has (usually 0), and according to its shape, I find the f(x) to use Fourier with.

    Please, anyone answer this, I've been trying to find it for the last 5 hours with no luck, the library is closed and my exam is tomorrow morning. And I apologize for the lack of LATeX.


  2. jcsd
  3. Feb 23, 2004 #2

    Tom Mattson

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    It would help if you would state the problem as it appears in the book.
  4. Feb 23, 2004 #3

    It's not a problem from a book, it's just the physical description of of oscillations of gas in a tube solved using Fourier analysis. It is not explained in the books I have, and I couldn't find the step by step analysis online (the usual example is a string) so that's why I asked. Anyway, my exam was this morning. Thanks.

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook