When two progressive waves of intensity $I_{1}$ and $I_{2}$ but slightly different frequencies superpose, the resultant intensity fluctuates between

{(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2}

and

{(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2}

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(\sqrt{I_{1}} - \sqrt{I_{2}})

and

(\sqrt{I_{1}} + \sqrt{I_{2}})

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(I_{1} + I_{2})

and

(I_{1} - I_{2})

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(I_{1} + I_{2})^{2}

and

(I_{1} - I_{2})^{2}

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Solution

The correct option is B ${(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2}$ and ${(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2}$
The resultant amplitude can be given by $A = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cos (ϕ)}$ .
So, the maximum amplitude is $A_{m a x} = (A_{2} + A_{1}) \Rightarrow I_{m a x} = (\sqrt{I_{2}} + \sqrt{I_{1}})^{2}$
and minimum amplitude is $A_{m i n} = (A_{1} - A_{2}) \Rightarrow I_{m i n} = (\sqrt{I_{1}} - \sqrt{I_{2}})^{2}$

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Similar questions

i = i_{1} cos ω t + i_{2} sin ω t

Now what should be the correct relation between $I_{1}$ , $I_{2}$ and $I_{3}$ .

I_{1}

I_{2}

α

\frac{I_{1}}{I_{2}}

I = 4 I_{0} {cos}^{2} \frac{ϕ}{2}

\frac{I_{m a x}}{I_{m i n}} = \frac{{(\sqrt{I_{1}} + \sqrt{I_{2}})}^{2}}{{(\sqrt{I_{1}} - \sqrt{I_{2}})}^{2}}

I_{1} = π / 2 \int 0 cos (sin x) d x; I_{2} = π / 2 \int 0 sin (cos x) d x

I_{3} = π / 2 \int 0 cos x d x,

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