# Interference: Resultant intensity.

1. Oct 16, 2009

### physlol

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

To waves with the same frequency interfere. The intensity of the two waves are I1 and I2. Show that the resultant intensity is:

I = I1 +I2 + 2*sqrt(I1*I2)*cos(δ)

Where δ is the phase difference between the two waves.

Hint: Use the relation between intensity and amplitude.

2. Relevant equations

None given, except the one above.

3. The attempt at a solution

Tried alot, but i really don't have a clue. Firstly: What is the relation between intensity and amplitude?

And I'm sorry for my language. English, as well as physics obviously, are not mye favourite subjects :)

2. Oct 16, 2009

### rl.bhat

Hi physlol, welcome to PF.
You have said that you tried a lot, but you have not shown any attempt. Even you have not opened the text book to see the relation between intensity and amplitude.
Amplitudes behave like vectors. Do you know how to find the resultant of two vectors having an angle θ between?
Collect these information and come back. We will helpyou.

3. Oct 16, 2009

### physlol

Yes, I did try. Yes, I have opened my textbook( Physics for scientists and engineers, Tipler & Mosca). But I did not find anything that helped me. So I've been sitting here, trying to get something usefull out of playing around with formulas that i dont have think will work.

This I did not know. I dont know how this would help me, though.

Yes.

4. Oct 16, 2009

### rl.bhat

Well. I am surprised to know that in the interference chapter they are not discussing the relation between intensity and amplitude, constructive and destructive interference.
Any way intensity is proportional to square of amplitude.
If two wave have A1 and A2 with pηase difference δ, find the resultant amplitude.
Then convert this into intensity.

5. Oct 16, 2009

### physlol

I am able to prove that the equation is correct if both the amplitudes that interfere are equal by using A2 = p0 + Cos(0,5*δ).

But they do not have to be equal i assume, and therefor I am kinda lost on how to come up with an expression for the resultant amplitude that I can convert to intensity.

I am sorry if there is something obvious that I have overlooked, but physics is really not my strongest subject.

6. Oct 16, 2009

### rl.bhat

You have told that you know how to find the resultant of two vectors.
Find the resultant of vector A1 and A2 having angle between them δ.