Solving a problem of chapter 9 DJ Griffith (linear combinations of sinusoidal waves)

[Zeeshan Ahmad]

Homework Statement:

Obtain eq 20(show in the below picture)
Directly from the waves equation by separation of variable

Relevant Equations:

linear combinations of sinusoidal waves

While I was doing a problems of chapter 9 of DJ griffith electrodynamics

I came across this problem 4
Problem statement
Obtain eq 20(show in the below picture)
Directly from the waves equation by separation of variable

Could I have a straight solution in your word
Thank you

 

[vanhees71]

No, but some help to find the solution yourself. Roughly speaking you just need to do two steps (which are always the same for such linear partial differential equations!):

(a) write down the wave equation
(b) write down the separation ansatz, plug it into the wave equation and find the corresponding mode functions

 

[vela]

Are you familiar with the method of separation of variables for solving PDEs? It's definitely something you should learn, if not.

 

[Zeeshan Ahmad]

I have posted it in the morning and done it up till when I got response to it
But thanks for the response 😊
From mr vanhees and vela