(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that the function [tex]u(x,y,z,t)=f(\alpha x + \beta y + \gamma z \mp vt)[/tex] where [tex]\alpha ^2 + \beta ^2 + \gamma ^2 =1[/tex] satisfies the tridimensional wave equation if one assume that f is differentiable twice.

2. Relevant equations

[tex]\frac{\partial ^2 u}{\partial t ^2}-c^2 \triangle u=0[/tex].

3. The attempt at a solution

I'm not sure how to use the chain rule.

[tex]\frac{\partial u}{\partial t}=\frac{\partial f}{\partial t}=\mp v \frac{\partial f}{\partial \sigma}[/tex] where [tex]\sigma =vt[/tex]. Thus [tex]\frac{\partial ^2 u}{\partial t ^2}=v^2 \left ( \frac{\partial f}{\partial \sigma} \right ) ^2[/tex].

I'm 98% sure it's not right.

Am I approaching well the problem?

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# Homework Help: Wave equation problem

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