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In the case of interference, the maximum and minimum intensities are in the ratio 16:9. Then

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The amplitudes of the individual waves will be in the ratio 7 : 1

The maximum and minimum amplitudes will be in the ratio 9 : 5

The intensities of the individual waves will be in the ratio 4 : 3

The amplitudes of the individual waves will be in the ratio 4:1

answer is C.

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Detailed Solution

The given values are

$I_{\max} = 16$

$I_{\min} = 9$

$\frac{I_{\max}}{I_{\min}} = \frac{16}{9}$

$\frac{I_{\max}}{I_{\min}} = {[\frac{\sqrt{I_{1}} + \sqrt{I_{2}}}{\sqrt{I_{1}} - \sqrt{I_{2}}}]}^{2} = {[\frac{a_{1} + a_{2}}{a_{1} - a_{2}}]}^{2}$

${[\frac{a_{1} + a_{2}}{a_{1} - a_{2}}]}^{2}$ = $\frac{16}{9}$

$\frac{a_{1} + a_{2}}{a_{1} - a_{2}} = \frac{4}{3}$

$\Rightarrow \frac{a_{1}}{a_{2}} = \frac{7}{1}$

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