Question

Ratio of intensities of two waves is $9:1$. If these two are superimposed, what is the ration of maximum and minimum intensities

• A. $3:1$
• B. $4:9$
• C. $4:1$
• D. $1:9$

Answer 1

The correct option is C $4:1$

Given,

$\frac{I_1}{I_2}={\left(\frac{a_1}{a_2}\right)}^2=\frac{9}{1}\frac{a_1}{a_2}=\frac{3}{1}\Rightarrow a_1=3a_2--------\left(i\right)\frac{I_{max}}{I_{min}}=\frac{(a_1+a_2{)}^2}{(a_1-a_2{)}^2}=\frac{(3a_2+a_2{)}^2}{(3a_2-a_2{)}^2}={\left(\frac{4a_2}{2a_2}\right)}^2=\frac{4}{1}$

Hence the required ratio is 4:1.