- #1
Briguy21
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Homework Statement
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
Homework Equations
laplacian= d^2phi/dx^2 + d^2phi/dy^2 + d^2phi/dz^2
only interested in d^2phi/dx^2
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!