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Electromagnetic waves

  • #1
438
0

Homework Statement



The electric components E1 and E2 of two coherent electromagnetic waves are given as follows :

[tex]E_1=E_o\sin (\omega t-kx)[/tex]

[tex]E_2=E_o\sin (\omega t-k(x+\delta))[/tex]

These two waves superpose each other at a certain point . Derive the amplitude of the resultant wave in terms of k and delta .

Homework Equations





The Attempt at a Solution



I tried adding them using the sin formulas , but i failed to express it in the form of

[tex]A \cos \theta \sin \omega t [/tex]
 

Answers and Replies

  • #2
ehild
Homework Helper
15,406
1,810
The sum of the two waves can be substituted by a single one of the same angular frequency w and wavenumber k, that is

[tex]
E_o\sin (\omega t-kx)+E_o\sin (\omega t-k(x+\delta))= A\sin (\omega t-k(x+\alpha))
[/tex].

You have to find the expression of A in terms of E0 and delta.

ehild
 
  • #3
438
0
The sum of the two waves can be substituted by a single one of the same angular frequency w and wavenumber k, that is

[tex]
E_o\sin (\omega t-kx)+E_o\sin (\omega t-k(x+\delta))= A\sin (\omega t-k(x+\alpha))
[/tex].

You have to find the expression of A in terms of E0 and delta.

ehild
thanks ehild , but i don really get it , i don see where is the alpha coming from ..
 
  • #4
ehild
Homework Helper
15,406
1,810
Alpha is a phase constant for the new wave. You can determine both alpha and the amplitude A by using the identity for the sine of the difference of angles. Have you learnt how to do it?

ehild
 

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