The ratio of intensities of two waves is 16 : 1. If these two are superimposed, what is the ratio of maximum and minimum intensities?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 25 : 9
Intensity is proportional to the square of the amplitude. When the waves superpose, the amplitudes (not the intensities) add in constructive interference and subtract in destructive interference.
\( \displaystyle \frac{a_1}{a_2} = \sqrt{\frac{I_1}{I_2}} = \sqrt{16} = 4 \)
\( \displaystyle \frac{I_{\max}}{I_{\min}} = \frac{(a_1 + a_2)^{2}}{(a_1 - a_2)^{2}} = \frac{(4+1)^{2}}{(4-1)^{2}} = \frac{25}{9} \)