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  • Two Periodic waves of intensities 4 and 8 pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities isOption:

Two Periodic waves of intensities 4 and 8 pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

Option: 1

I_{\max }+I_{\min }=24


Option: 2

I_{\max }+I_{\min }=20


Option: 3

I_{\max }+I_{\min }=25


Option: 4

I_{\max }+I_{\min }=23


Answers (1)

best_answer

$$ \begin{aligned} & I_{\max }=\left(\sqrt{I_{1}}+\sqrt{I_{2}}\right)^{2} \\ & I_{\min }=\left(\sqrt{I_{1}}-\sqrt{I_{2}}\right)^{2} \\ & I_{\text {max }}+I_{\min }=\left(\sqrt{I}+\sqrt{I_{2}}\right)^{2}+\left(\sqrt{I_{1}}-\sqrt{I_{2}}\right)^{2} \\ & =I_{1}+I_{2}+2 \sqrt{I_{1} \cdot I_{2}}+I_{1}+I_{2}-\sqrt{2 I_{1}} I_{2} \\ & 2 I_{1}+2 I_{2} \\ & 2\left(I_{1}+I_{2}\right) \\ & \text { max }+ \text { Imit }=2(4+8) \\ & 2 \times 12=24 \\ & I_{\max }+I_{\min }=24 \end{aligned}

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Ajit Kumar Dubey

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