How to Calculate the Amplitude of a Resultant Electromagnetic Wave?

[thereddevils]

Homework Statement

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

$$E_1=E_o\sin (\omega t-kx)$$

$$E_2=E_o\sin (\omega t-k(x+\delta))$$

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

$$A \cos \theta \sin \omega t$$

 

[ehild]

The sum of the two waves can be substituted by a single one of the same angular frequency w and wavenumber k, that is

$$E_o\sin (\omega t-kx)+E_o\sin (\omega t-k(x+\delta))= A\sin (\omega t-k(x+\alpha))$$.

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

ehild

 

[thereddevils]

The sum of the two waves can be substituted by a single one of the same angular frequency w and wavenumber k, that is

$$E_o\sin (\omega t-kx)+E_o\sin (\omega t-k(x+\delta))= A\sin (\omega t-k(x+\alpha))$$.

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 ..

 

[ehild]

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 learned how to do it?

ehild