Interference: Resultant intensity.

[physlol]

Homework Statement

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.

Homework Equations

None given, except the one above.

The Attempt at a Solution

Tried a lot, 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 :)

 

[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 textbook 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.

 

[physlol]

You have said that you tried a lot, but you have not shown any attempt. Even you have not opened the textbook to see the relation between intensity and amplitude.

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 don't have think will work.

Amplitudes behave like vectors.

This I did not know. I don't know how this would help me, though.

Do you know how to find the resultant of two vectors having an angle θ between?

Yes.

 

[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.

 

[physlol]

Thanks for the reply.

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.

 

[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.