# Seismic displacement ofr a plane wave

1. Nov 3, 2008

### Briguy21

1. The problem statement, all variables and given/known data
phi(x,y,z,t)= cos(wt- the dot product of K and x)
k= kx i hat + ky j hat + kz k hat units are m^-1
x= x i hat + y j hat + z k hat units are m

t is time and w is the angular velocity w/ units of sec^-1

show that abs. value of k = w/alpha by plugging the displacement potential into the P-wave equation:

laplacian(phi) = 1/alpha^2 times d^2phi/dt^2

2. Relevant equations
laplacian= d^2phi/dx^2 + d^2phi/dy^2 + d^2phi/dz^2
only interested in d^2phi/dx^2

3. The attempt at a solution
I have carried out the dot product of k dot x:
x, y, z= sub x, y, z
X,Y,Z= X, Y, and Z
cos(wt-kxX + kyY + KzZ)

now I am stuck and don't know where to go/what to do...... any tips/suggestions would be awesome!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Nov 3, 2008

### gabbagabbahey

Well, you have: $\varphi(\vec{x},t)=Cos(\omega t- k_x x-k_y y -k_z z)$ so why not find $\frac{\partial \varphi}{\partial t}$ and $\nabla ^2 \varphi$ and see what $\alpha$ must be if $\varphi$ satisfies your given wave equation?