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Two monochromatic waves, each of amplitude a, have random phase difference between them. When these superpose, then the amplitude of resultant wave is given by a) root2 a b) 2a c) 4a d) zero

Two monochromatic waves, each of amplitude a, have random phase difference between them. When these superpose, then the amplitude of resultant wave is given by
a) root2 a
b) 2a
c) 4a
d) zero

Grade:12

1 Answers

Rituraj Tiwari
askIITians Faculty 1792 Points
2 years ago
(A net )^2= (A1)^2+ (A2)^2 + 2(A1A2)cosX....

So,

(A net )^2= (A1)^2+ (A2)^2

Here since source is coherent.... A1 = A2 = A....

So ,

(A net )^2= (A)^2+ (A)^2

(A net )^2= 2(A)^2

And therefore...

A net ( or resultant amplitude) = (2)^1/2 *A

Option (a) is therefore correct.

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