I am new to wave mechanics in 2 and 3 dimensions and would like to know: Do you simply add $\partial \psi \over\partial y$ and/or $\partial \psi \over\partial z$ term without the other parts of the equation changing? By changing I mean specifically about the expression for the phase velocity. I get that the phase velocity for electromagnetic waves should always be $1\over\sqrt{\mu_0\varepsilon_0}$, and by isomorphism we should have the phase velocity expressions for other types of waves be the same in 1, 2, and 3 dimensions. Is this the correct way to think about it?
Electromagnetism – Wave Equation in 2D and 3D
electromagnetic-radiationelectromagnetismwaves
Best Answer
The wave equation contains the second derivatives in respect to position. So, you have the Laplace operator applied to the function (your $\psi$ ) that expreses the displacement from equilibrium, in either 2D or 3D. Nothing changes for the derivative in respect to time.