# destructive inteference

#### ling233

i dont understand why the intensity of waves due to destructive inteference is still 2(A^2 ).... since this is destructive inteference why not the wave intensity=0?

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anyone here?

#### ChipB

PHF Helper
2A^2 is the average intensity for two waves of amplitude A that are 60 degrees apart. It would be zero if the two waves were 180 degrees apart.

#### ling233

2A^2 is the average intensity for two waves of amplitude A that are 60 degrees apart. It would be zero if the two waves were 180 degrees apart.
why average intensity is used? and i dont understand how is the average intensity calculated.

#### ChipB

PHF Helper
I think all they were trying to show with the calculation of average intensity is that conservation of energy still applies, so the average intensity is equal to the sum of the intensity of the two individual waves. To find this average they determine the amplitude of the wave at two separate points - one where the waves are 60 degrees apart and another where they are 60+180 = 240 degrees apart. Mathematically they do this by first adding the two vectors (to get intensity = sqrt(3)A^2 and then by subtracting one from the other (to get intensity = A^2. Then they take the average of the two. This method works for any value of phase angle - for any point that has intensity of kA^2 there is another point that has intensity (4-k^2)A^2, for an average between the two points of 2A^2.

#### ling233

can you draw a diagram showing the phase difference =120 degree? it's rather hard for me to imagine this as I dont understand the question very well

#### ChipB

PHF Helper
Here you go. The upper image is A1+A2, and the lower is A1-A2.

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#### ling233

Here you go. The upper image is A1+A2, and the lower is A1-A2.
the A1+ A2=3A^2 , but what do you mean by then by subtracting one from the other (to get intensity = A^2 ? still blurred now

#### ling233

Here you go. The upper image is A1+A2, and the lower is A1-A2.
do you mean the author is finding the average intensity of constructive superposition and desrtuctive superposition? where constructive superposition leads to 3A^2 , and destructive superposition leads to A^2 ?

#### ling233

for the first photo, why cant I get PR=(A^2) +(A^2)-2(A^2)COS60 ? as i saw, the angle between A1 AND A2 is 60...