Adding waves of the same frequency but different phases

[lcr2139]

Homework Statement

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)[/B]

Homework Equations

Er = E1 + E2[/B]

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)
?[/B]

 

[RUber]

Homework Statement

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)[/B]

Homework Equations

Er = E1 + E2[/B]

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)
?[/B]

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.

 

[insightful]

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

Try it, then shift your answer back 70^o, and check your answer.

 

[nasu]

How do you add waves "that only have one phase"?