Graphing the Wave Equation with Quadratic Functions

[jonroberts74]

Homework Statement

set \phi = f(x-t)+g(x+t)

a) prove that \phisatisfies the wave equation : \frac{\partial^2 \phi}{\partial t^2} = \frac{\partial^2 \phi}{\partial x^2}

b) sketch the graph of \phi against t and x if f(x)=x^2 and g(x)=0

The Attempt at a Solution

part a, I have already gotten the answer to; just posting that so that the second part makes some sense.

I don't really know how to do part b, the two functions given don't have a t, so not sure how I graph phi against x and t

 

[LCKurtz]

Homework Statement

set \phi = f(x-t)+g(x+t)

a) prove that \phisatisfies the wave equation : \frac{\partial^2 \phi}{\partial t^2} = \frac{\partial^2 \phi}{\partial x^2}

b) sketch the graph of \phi against t and x if f(x)=x^2 and g(x)=0

The Attempt at a Solution

part a, I have already gotten the answer to; just posting that so that the second part makes some sense.

I don't really know how to do part b, the two functions given don't have a t, so not sure how I graph phi against x and t

If $f(x) = x^2$ and $g(x) = 0$, then $\phi(x,t) = (x-t)^2$. Plot that as a 3D surface with $\phi$ in the $z$ direction and $x$ and $t$ as the two independent variables.

 

[jonroberts74]

so its a parabolic cylinder?