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Old Jan 28th 2017, 08:08 AM   #1
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1D wave equation problem

Hello-

I'm having trouble understanding a problem:

Consider a sealed 1D pipe of length L. At t=0, v=0 everywhere and the pressure is given by: P=P_0 +δP

and δP = (p-bar)x/L

P_0 and (p-bar) are both constants.

and I'm supposed to find density (ϱ) as a function of x and t.

I don't understand why I'm given the pressure, and how to find δϱ.

Last edited by jlee07; Jan 28th 2017 at 08:11 AM.
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Old Jan 29th 2017, 12:14 PM   #2
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1D wave equation problem

The solution to this is a harmonic function. (Cos and sine wave or e^ipix). This is a common solution to the wave equation and it should be possible for you to find a formula for an accoustic pulse wave as this is the most simple scenario.

You will use fourier series to approximate the given initial conditions as the pressure increases linearly along the length. i.e. summation of harmonic functions to approximate the given initial conditions. This will enable you to calculate properties such as density at position x and time t based on the summation of the harmonic functions.
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Old Jan 30th 2017, 02:19 PM   #3
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The density will of course depend on the fluid in the pipe,
which you don't mention in your post.
see this wikipedea link: <Density as a Function of Pressure in a Gas>
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