# Phase constant for light waves

1. Aug 26, 2011

### roam

1. The problem statement, all variables and given/known data

We have two waves with functions:

$$E_1 = 6 \ sin (100 \pi t)$$

$$E_2 = 8 \ sin (100 \pi t + \frac{\pi}{2})$$

Find $$E_1 + E_2$$.

2. Relevant equations

$$\phi = \frac{2 \pi}{\lambda} \delta = \frac{2 \pi}{\lambda} d sin \theta$$

$$\frac{\delta}{\lambda}=\frac{\phi}{2 \pi}$$

3. The attempt at a solution

The answer to this problem should be $$10 \ sin (100 \pi t + 0.927)$$
I can't understand how they got the value for the phase constant phi to be 0.927. I can't understand how they got the value using the above equations... because we don't know and can't find many variables in those equations. And I'm not sure how to use trig fro this... Any help with this problem is greatly appreciated.

2. Aug 26, 2011

### Pi-Bond

Let

$E_1 + E_2 = Asin(100 \pi t + B)$

Use this and compare coefficients to get the values of A and B. You might want to use the sine addition formula on $E_2$ to first simplify that expression.

3. Aug 26, 2011

### mstud

Last edited by a moderator: Apr 26, 2017