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(B) Let the intensities of the two waves be $I_A = I_0$ and $I_B = 9I_0$.For incoherent waves,the resultant intensity is the sum of individual intensi

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$13$

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(B) Let the intensities of the two waves be $I_A = I_0$ and $I_B = 9I_0$.For incoherent waves,the resultant intensity is the sum of individual intensities:$I_1 = I_A + I_B = I_0 + 9I_0 = 10I_0$.For coherent waves,the resultant intensity is given by $I_2 = I_A + I_B + 2\sqrt{I_A I_B} \cos \phi$,where $\phi = 60^{\circ}$.$I_2 = I_0 + 9I_0 + 2\sqrt{I_0 \cdot 9I_0} \cos 60^{\circ}$.$I_2 = 10I_0 + 2(3I_0) \cdot \frac{1}{2} = 10I_0 + 3I_0 = 13I_0$.Given $\frac{I_1}{I_2} = \frac{10}{x}$,we have $\frac{10I_0}{13I_0} = \frac{10}{x}$.Therefore,$x = 13$.

Two waves of intensity ratio $1:9$ cross each other at a point. The resultant intensities at the point are $I_1$ when the waves are incoherent and $I_2$ when the waves are coherent with a phase difference of $60^{\circ}$. If $\frac{I_1}{I_2} = \frac{10}{x}$,then $x = . . . . . . . . . . .$

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