- #1
roldy
- 237
- 2
Homework Statement
Two part problem
(1)
For a plane wave [tex]\vec{u}=Ue^{j(\omega{t}-kx)}[/tex].
Find expressions for the acoustic Mach number U/c in terms of...
(a) P, [tex]\rho_o[/tex], and c.
(b) s
(2)
If [tex]\vec{p}=Pe^{j(\omega{t}-kx)}[/tex] find,
(a) the acoustic density
(b) the particle speed
(c) the velocity potential
Homework Equations
[tex]
c=\sqrt{\gamm,a{R}T}
P=\rho{R}{T}
\Phi=j\left(\frac{P}{\rho_o}e^{j(\omega{t}-kx)}
P=-\rho\frac{\partial \Phi}{\partial t}
\vec{u}=\nabla{\Phi}
[/tex]
The Attempt at a Solution
(1)
I have no idea how to start this. I've been reading the class notes (which are horrible) and the book (horrible as well) and I couldn't find anything that would help me get started. I've tried searching on google but I was given the run around. Any help would be awesome.
(2)
I've only come this far...
(a)
[tex]
\rho-\rho_o=\frac{1}{c_o^2}\tilde{p}
=\frac{1}{c_o^2}Pe^{j(\omega{t}-kx)}
[/tex]
(b) I know I can probably figure this one out if I knew how to do part (1). I just need to rework the pressure equation in terms of velocity. Am I correct in this assumption.
(c)
[tex]
\nabla\times\vec{u}=0
\vec{u}=\nabla\Phi
[/tex]
I wish I could of showed more on these problems but I'm really lost with this material.