- #1
dustydude
- 19
- 0
Homework Statement
hey I am having trouble figuring this out. The question states that i am to find the second component of velocity?
there is a plane wave incident on a surface at (0,0).
Homework Equations
the incident potential is
[tex]\Psi^{I} (x,t)= A\, e^{-i\omega (t- \frac{1}{c}(x\,sin\theta -y\,cos\theta)) }[/tex]
the reflected potential is
[tex]\Psi^{R} (x,t)= A\, e^{-i\omega (t- \frac{1}{c}(x\,sin\theta +y\,cos\theta)) }[/tex]
theta is the angle which the wave makes with the y axis.
i think there is an assumption that
[tex]\triangledown \times \mathbf{u} = 0[/tex] such that [tex]\mathbf{u}=\triangledown \Psi [/tex]
The Attempt at a Solution
First is the total velocity potential then just,
[tex]\Psi= \Psi^{I}+ \Psi^{R}[/tex]
and then the second component of u would be
[tex] \frac{\partial } {\partial y}(\Psi^{I}+\Psi^{R})[/tex]