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(B) The source at $S$ generates a wave of intensity $I_0$. This intensity is equally divided into two parts,so each part has an intensity $I = I_0 / 2

Vedclass · Accepted Answer

$2I_0$

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(B) The source at $S$ generates a wave of intensity $I_0$. This intensity is equally divided into two parts,so each part has an intensity $I = I_0 / 2$.Since intensity $I$ is proportional to the square of the amplitude $A$ $(I \propto A^2)$,the amplitude of each wave is $A = \sqrt{I} = \sqrt{I_0 / 2}$.When these two waves meet at point $D$,they interfere. The resultant intensity $I_{res}$ is given by the formula $I_{res} = I_1 + I_2 + 2\sqrt{I_1 I_2} \cos \phi$,where $\phi$ is the phase difference.For maximum intensity,the waves must interfere constructively,meaning $\cos \phi = 1$.Thus,$I_{max} = I_1 + I_2 + 2\sqrt{I_1 I_2} = (\sqrt{I_1} + \sqrt{I_2})^2$.Substituting $I_1 = I_2 = I_0 / 2$:$I_{max} = (\sqrt{I_0 / 2} + \sqrt{I_0 / 2})^2 = (2 \sqrt{I_0 / 2})^2 = 4 	imes (I_0 / 2) = 2I_0$.

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