Three light waves combine at a point find resultant amplitude and phase angle

[CianM]

Homework Statement

Three light waves combine at a point where their electric field components are

E₁ = E_o$$sin \omega$$t

E₂ = E_o$$sin (\omega$$t - 2$$\pi$$/3)

E₃ = E_o$$sin (\omega$$t + $$\pi$$/3)

Find the resultant amplitude of the electric field E_R at that point and it's phase angle$$\beta$$
Write the resultant wav int the form E = E_R$$sin(\omega$$t + $$\beta$$)

Homework Equations

The Attempt at a Solution

Am I right in assuming that first you add E₁+E₂ then add E₁₂ + E₃ using double angle formulas? Or am I going about this completely the wrong way?

 

[denverdoc]

What about adding all three at once, using dbl angle formula to break out the phase shifts and collecting like terms. The results should be the same.

 

[CianM]

Well I already did the way I suggested and the answer I got was :
E_R = 2E_o sin ($$\omega$$t)cos($$\pi$$/3)
taking cos($$\pi$$/3) = 1/2
then equals E_R = E_osin( $$\omega$$t) .
Is this right?

 

[denverdoc]

yep, some careful examination of the problem shows that the -phase shift term is equal and opposite to the positive shift term, cancelling out, leaving your result. (in other words the two phase angles sum to pi)

 

[CianM]

Ok. Thanks for your help!