Register to reply 
Solution of wave equation, 2nd partial derivatives of time/position 
Share this thread: 
#1
Apr113, 04:45 PM

P: 110

f(z,t)=\frac{A}{b(zvt)^{2}+1}...
\frac{\partial^{2} f(z,t)v^{2} }{\partial z^2}=\frac{2Abv^{2}}{[b(zvt)^{2}+1]^{2}}+\frac{8Ab^{2}v^{2}(zvt)^{2}}{[b(zvt)+1]^{3}}=\frac{\partial^2 f}{\partial t^2} \frac{2Abv^{2}}{[b(zvt)^{2}+1]^{2}}+\frac{8Ab^{2}v^{2}(zvt)^{2}}{[b(zvt)+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! 


#2
Apr913, 10:22 AM

P: 110

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)....



Register to reply 
Related Discussions  
General solution to partial differential equation (PDE)  Differential Equations  1  
Using Partial Derivatives To Prove Solution To Wave Equation  Calculus & Beyond Homework  6  
Help with solution to partial differential equation  Calculus & Beyond Homework  6  
Ordinary (Or Partial) Differential Equation Unique Solution  Calculus & Beyond Homework  13  
Solution to partial differential equation  Differential Equations  0 