Superposition

1. Two coherent waves of intensities I and 2I meet in phase at a point. Given that intensity is proportional to (amplitude) ^2 for these waves, calculate, in terms of I, the intensity of the resultant wave at that point.

Can anyone please explain this to me? I know that if I is directly proportional to (3/2A0^2 then it should be 9/4A .. . but the answer given is 9/4I. So I think I don't really understand this concept. Plz help me! thx

The answer is wrong.
The first thing is understand taht Intensities don't add up. Amplitudes add.
So we have to find the amplitudes of the two waves.
So take the square root, this gives
A and 2^1/2A
add them together gives
(1+2^1/2)A
Square it to get the Intensity
[(1+2^1/2)A]² = [(1+2^1/2)²I
= (3+8^1/2)I

The answer is wrong.
The first thing is understand taht Intensities don't add up. Amplitudes add.
So we have to find the amplitudes of the two waves.
So take the square root, this gives
A and 2^1/2A
add them together gives
(1+2^1/2)A
Square it to get the Intensity
[(1+2^1/2)A]² = [(1+2^1/2)²I
= (3+8^1/2)I

The answer is wrong.
The first thing is understand taht Intensities don't add up. Amplitudes add.
So we have to find the amplitudes of the two waves.
So take the square root, this gives
A and 2^1/2A
add them together gives
(1+2^1/2)A
Square it to get the Intensity
[(1+2^1/2)A]² = [(1+2^1/2)²I
= (3+8^1/2)I

sorry just interested and just found this aswell and dont fully understand this, why do we root the amplitude ?? thanks.

Not sure really what you mean by taking the root of the amplitude.

We are given that “Given that intensity is proportional to (amplitude) ^2 for these waves”, so if the intensity is I, then assume the associated amplitude is A.

For 2I,


then the amplitude would be $\sqrt{2} A$.