(adsbygoogle = window.adsbygoogle || []).push({}); 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.

Thanks,

Sol.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**