Question

Two coherent sources of different intensities send waves which interfere. The ratio of maximum intensity to the minimum intensity is 25. The intensities of the sources are in the ratio

• A. 25:01:00
• B. 5:01
• C. 9:04
• D. 25:16:00

Answer 1

The Correct Option is C

Let $a_1 $ and $ a_2$ be amplitudes of the two waves. For maximum intensity $\hspace30mm I_{max} = (a_2 + a_2)^2$ For minimum intensity $\hspace30mm I_{min} = (a_2 - a_2)^2$ Given, $\hspace20mm \frac{I_{max}}{I_{min}} = \frac{25}{1} = \frac{((a_1 + a_2)^2)}{(a_1 - a_2)^2}$ $\Rightarrow \hspace20mm \frac{a_1 + a_2}{a_1 - a_2} = \frac{5}{1} \Rightarrow \frac{a_1}{a_2} = \frac{3}{2}$ $\therefore \hspace30mm \frac{I_1}{I_2} = \frac{a_1^2}{a_2^2} = \big(\frac{3}{2}\big)^4 = \frac{9}{4}$