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(C) Given the ratio of intensities of two waves is $\frac{I_1}{I_2} = \frac{9}{4}$.Since intensity $I \propto a^2$,the ratio of amplitudes is $\frac{a

Vedclass · Accepted Answer

$25: 1$

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(C) Given the ratio of intensities of two waves is $\frac{I_1}{I_2} = \frac{9}{4}$.Since intensity $I \propto a^2$,the ratio of amplitudes is $\frac{a_1}{a_2} = \sqrt{\frac{I_1}{I_2}} = \sqrt{\frac{9}{4}} = \frac{3}{2}$.The maximum intensity is $I_{max} = (a_1 + a_2)^2$ and the minimum intensity is $I_{min} = (a_1 - a_2)^2$.The ratio of maximum to minimum intensity is $\frac{I_{max}}{I_{min}} = \frac{(a_1 + a_2)^2}{(a_1 - a_2)^2} = \left( \frac{a_1 + a_2}{a_1 - a_2} \right)^2$.Substituting the values,$\frac{I_{max}}{I_{min}} = \left( \frac{3 + 2}{3 - 2} \right)^2 = \left( \frac{5}{1} \right)^2 = \frac{25}{1}$.Thus,the ratio is $25: 1$.

The ratio of intensities of two waves producing interference is $9: 4$. The ratio of the resultant maximum and minimum intensities will be:

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