Acoustics: Plane Wave Homework | Expressions, Equations & Solutions

[roldy]

Homework Statement

Two part problem

(1)
For a plane wave $$\vec{u}=Ue^{j(\omega{t}-kx)}$$.
Find expressions for the acoustic Mach number U/c in terms of...
(a) P, $$\rho_o$$, and c.
(b) s

(2)
If $$\vec{p}=Pe^{j(\omega{t}-kx)}$$ find,
(a) the acoustic density
(b) the particle speed
(c) the velocity potential

Homework Equations

$$c=\sqrt{\gamm,a{R}T}<br /> P=\rho{R}{T}<br /> \Phi=j\left(\frac{P}{\rho_o}e^{j(\omega{t}-kx)}<br /> P=-\rho\frac{\partial \Phi}{\partial t}<br /> \vec{u}=\nabla{\Phi}$$

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)
$$\rho-\rho_o=\frac{1}{c_o^2}\tilde{p}<br /> =\frac{1}{c_o^2}Pe^{j(\omega{t}-kx)}$$

(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)
$$\nabla\times\vec{u}=0<br /> \vec{u}=\nabla\Phi$$

I wish I could of showed more on these problems but I'm really lost with this material.

 

[roldy]

Any suggestions?