If the ratio of maximum to minimum resultant intensity in interference pattern of two waves is 25 : 4, then, ratio of amplitudes two waves is :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 7 : 3
In interference the resultant amplitude is \( a_1 + a_2 \) at a maximum and \( a_1 - a_2 \) at a minimum, and intensity is proportional to the square of the amplitude.
\( \displaystyle \frac{I_{\max}}{I_{\min}} = \frac{(a_1 + a_2)^2}{(a_1 - a_2)^2} = \frac{25}{4} \)
Taking the square root:
\( \displaystyle \frac{a_1 + a_2}{a_1 - a_2} = \frac{5}{2} \)
\( 2a_1 + 2a_2 = 5a_1 - 5a_2 \)
\( 3a_1 = 7a_2 \)
\( \displaystyle \frac{a_1}{a_2} = \frac{7}{3} \)