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

1. Dec 7, 2009

### CianM

1. The problem statement, all variables and given/known data
Three light waves combine at a point where their electric field components are

E1 = Eo$$sin \omega$$t

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

E3 = Eo$$sin (\omega$$t + $$\pi$$/3)

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

2. Relevant equations

3. 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?

2. Dec 7, 2009

### 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.

3. Dec 7, 2009

### CianM

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

4. Dec 7, 2009

### 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)

Last edited: Dec 7, 2009
5. Dec 7, 2009