b
Other factors such as \(\omega\) and \(v\) remaining

the same, \(I=A^{2} \times \,constant\) \(K,\) or \(A=\sqrt{\frac{I}{K}}\)

On superposition

\(A_{\max }=A_{1}+A_{2} \text { and } A_{\min }=A_{1}-A_{2}\)

\(\therefore \quad A_{\max }^{2}=A_{1}^{2}+A_{2}^{2}+2 A_{1} A_{2}\)

\(\Rightarrow \frac{I_{\max }}{K}=\frac{I_{1}}{K}+\frac{I_{2}}{K}+\frac{2 \sqrt{I_{1} I_{2}}}{K}\)

\(A_{\min }^{2}=A_{1}^{2}+A_{2}^{2}-2 A_{1} A_{2}\)

\(\Rightarrow \frac{I_{\min }}{K}=\frac{I_{1}}{K}+\frac{I_{2}}{K}-\frac{2 \sqrt{I_{1} I_{2}}}{K} \therefore I_{\max }+I_{\min }=2 I_{1}+2 I_{2}\)