# Adding waves of the same frequency but different phases

1. Sep 11, 2015

### lcr2139

1. The problem statement, all variables and given/known data
how do you add two waves with the same frequency but different phases?
E1 = 7*sin(omega*t + 70degrees)
E2 = 13*sin*(omega*t + 65degrees)

2. Relevant equations
Er = E1 + E2

3. The attempt at a solution
I know how to add waves that only have one phase, i.e.
E1 = E01*sin(omega*t)
E2 = E02*sin(omega*t + phase difference)

Can I subtract 65-70 degrees to make it
E1= E01*sin(omega*t)
E2 = E02*sin(omega*t - 5degrees)
?

2. Sep 11, 2015

### RUber

Kind of...it depends on what sort of result you are looking for.
Normally to adjust the phase, you would need a shift in t.
For example, $\sin (\omega t + \phi) = \sin (\omega (t+\phi/\omega) )$
So, if you replace t with $\tau$, and define $\tau = t+ \phi / \omega$, then you can have a similar set up to what you are used to dealing with and then substitute the definition for tau back into your solution to get what you are looking for.

3. Sep 11, 2015