Two waves coming from two coherent sources,ha | vedclass

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(C) Given that the ratio of maximum intensity to minimum intensity is $\frac{I_{\max}}{I_{\min}} = 25$.The formula for the ratio of maximum to minimum

Vedclass · Accepted Answer

$9 : 4$

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(C) Given that the ratio of maximum intensity to minimum intensity is $\frac{I_{\max}}{I_{\min}} = 25$.The formula for the ratio of maximum to minimum intensity is $\frac{I_{\max}}{I_{\min}} = \frac{(a+b)^2}{(a-b)^2}$,where $a$ and $b$ are the amplitudes of the two waves.Setting the ratio equal to $25$,we have $\frac{(a+b)^2}{(a-b)^2} = \frac{25}{1}$.Taking the square root of both sides,we get $\frac{a+b}{a-b} = \frac{5}{1}$.Cross-multiplying gives $a + b = 5a - 5b$,which simplifies to $4a = 6b$,or $\frac{a}{b} = \frac{6}{4} = \frac{3}{2}$.Since intensity $I$ is proportional to the square of the amplitude $(I \propto a^2)$,the ratio of the intensities of the sources is $\frac{I_1}{I_2} = \frac{a^2}{b^2} = \left(\frac{3}{2}\right)^2 = \frac{9}{4}$.

Two waves coming from two coherent sources,having different intensities,interfere. The ratio of their maximum intensity to the minimum intensity is $25$. What is the ratio of the intensities of the sources?

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