Two waves have their amplitudes in the ratio | vedclass

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Question

(A) The intensity $I$ of a wave is proportional to the square of its amplitude $a$,i.e.,$I \propto a^2$.Given the ratio of amplitudes $\frac{a_1}{a_2}

Vedclass · Accepted Answer

$\frac{25}{16}$

Vedclass · Answer

(A) The intensity $I$ of a wave is proportional to the square of its amplitude $a$,i.e.,$I \propto a^2$.Given the ratio of amplitudes $\frac{a_1}{a_2} = \frac{1}{9}$.The ratio of maximum to minimum intensity is given by the formula:$\frac{I_{\max}}{I_{\min}} = \left( \frac{a_1 + a_2}{a_1 - a_2} \right)^2 = \left( \frac{\frac{a_1}{a_2} + 1}{\frac{a_1}{a_2} - 1} \right)^2$.Substituting the given ratio $\frac{a_1}{a_2} = \frac{1}{9}$:$\frac{I_{\max}}{I_{\min}} = \left( \frac{\frac{1}{9} + 1}{\frac{1}{9} - 1} \right)^2 = \left( \frac{\frac{10}{9}}{-\frac{8}{9}} \right)^2 = \left( -\frac{10}{8} \right)^2 = \left( -\frac{5}{4} \right)^2 = \frac{25}{16}$.

Two waves have their amplitudes in the ratio $1 : 9$. The maximum and minimum intensities when they interfere are in the ratio

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