- #1

- 232

- 1

## 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.