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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