solution of wave equation, 2nd partial derivatives of time/position

by mathnerd15
Tags: derivatives, equation, partial, solution, time or position, wave
 P: 108 f(z,t)=\frac{A}{b(z-vt)^{2}+1}... \frac{\partial^{2} f(z,t)v^{2} }{\partial z^2}=\frac{-2Abv^{2}}{[b(z-vt)^{2}+1]^{2}}+\frac{8Ab^{2}v^{2}(z-vt)^{2}}{[b(z-vt)+1]^{3}}=\frac{\partial^2 f}{\partial t^2} \frac{-2Abv^{2}}{[b(z-vt)^{2}+1]^{2}}+\frac{8Ab^{2}v^{2}(z-vt)^{2}}{[b(z-vt)+1]^{3}} this is a solution of the wave equation, but it can be written with the Laplacian. is this also a hyperbolic partial differential equation. Alembert derived the solution that 1D waves are the addition of right and left moving functions what is the meaning of the 2nd partial derivatives in respect to time and position which differ by v^2? (I wrote this on online Latex editor, the differentiation is in the attachment) thanks very much! Attached Thumbnails
 P: 108 so you can derive the speed c from the Maxwell equations which for an electromagnetic wave is the Weber/Kohrausch ratio 1/(epsilono*muo)^(1/2)....

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