Solving Problem 4 of DJ Griffiths Electrodynamics Chapter 9

Zeeshan Ahmad
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Thread moved from the technical forums, and the OP has been reminded to show their work.
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
IMG_20210916_113300.jpg

Could I have a straight solution in your word
Thank you
 
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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
 
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Likes vela and berkeman
Are you familiar with the method of separation of variables for solving PDEs? It's definitely something you should learn, if not.
 
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
 
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