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

(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.