Two waves having intensities in the ratio 25 | vedclass

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(C) Given the ratio of intensities of two waves is $\frac{I_1}{I_2} = \frac{25}{4}$.Let the amplitudes of the waves be $A_1$ and $A_2$. Since intensit

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$49:9$

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(C) Given the ratio of intensities of two waves is $\frac{I_1}{I_2} = \frac{25}{4}$.Let the amplitudes of the waves be $A_1$ and $A_2$. Since intensity $I \propto A^2$,the ratio of amplitudes is $\frac{A_1}{A_2} = \sqrt{\frac{I_1}{I_2}} = \sqrt{\frac{25}{4}} = \frac{5}{2}$.The ratio of maximum to minimum intensity is given by the formula $\frac{I_{\max}}{I_{\min}} = \left( \frac{A_1 + A_2}{A_1 - A_2} \right)^2$.Substituting the values,we get $\frac{I_{\max}}{I_{\min}} = \left( \frac{5 + 2}{5 - 2} \right)^2 = \left( \frac{7}{3} \right)^2 = \frac{49}{9}$.

Two waves having intensities in the ratio $25 : 4$ produce interference. The ratio of the maximum to the minimum intensity is

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