Other factors such as $\omega$ and v remaining the same, I = A² constant K, or A = $\sqrt {{I \over K}}$

On superposition

${A_{\max }} = {A_1} + {A_2}$ and ${A_{\min }} = {A_1} - {A_2}$

$\therefore A_{\max }^2 = A_1^2 + A_2^2 + 2{A_1}{A_2}$

$\Rightarrow {{{I_{\max }}} \over K} = {{{I_1}} \over K} + {{{I_2}} \over K} + {{2\sqrt {{I_1}{I_2}} } \over K}$

$A_{\min }^2 = A_1^2 + A_2^2 - 2{A_1}{A_2}$

$\Rightarrow {{{I_{\min }}} \over K} = {{{I_1}} \over K} + {{{I_2}} \over K} - {{2\sqrt {{I_1}{I_2}} } \over K}$

$\therefore {I_{\max }} + {I_{\min }} = 2{I_1} + 2{I_2}$