Question 471: Waves

Question

Two periodic waves of intensities $I$
1
and $I$
2
pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

Accepted Answer

Other factors such as $\omega $ and v remaining
the same, I = A
2
constant K, or A = $\sqrt {{I \over K}} $
On superposition
${A_{\max }} = {A_1} + {A_2}$ and ${A_{\min }} = {A_1} - {A_2}$
$ 	herefore 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}$
$ 	herefore {I_{\max }} + {I_{\min }} = 2{I_1} + 2{I_2}$

Answer

${\left( {\sqrt {{I_1}}  - \sqrt {{I_2}} } \right)^2}$

Answer

$2\left( {{I_1} + {I_2}} \right)$

Answer

${{I_1} + {I_2}}$

Answer

${\left( {\sqrt {{I_1}}  + \sqrt {{I_2}} } \right)^2}$

Waves

Two periodic waves of intensities I 1 and I 2 pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

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