Question

Two interfering waves have intensities in the ratio $9:1$. Then the ratio of maximum to maximum intensity is:

• A. $16:4$
• B. $4:2$
• C. $100:64$
• D. $10:8$

Answer 1

The correct option is A $16:4$

Let $l_1$ and $l_2$ be the intensities of the waves. The ratio of two waves,
$l_1:\_2=9:1.$

Ratio of maximum and minimum intensity will be,
$\frac{I_{\text{max}}}{I_{\text{min}}}={\left(\frac{\sqrt{I_1}+\sqrt{I_2}}{\sqrt{I_1}-\sqrt{I_2}}\right)}^2$

$\frac{I_{\text{max}}}{I_{\text{min}}}={\left(\frac{\sqrt{9}+\sqrt{1}}{\sqrt{9}-\sqrt{1}}\right)}^2$

$\frac{I_{\text{max}}}{I_{\text{min}}}={\left(\frac{3+1}{3-1}\right)}^2$

$\frac{I_{\text{max}}}{I_{\text{min}}}={\left(\frac{4}{2}\right)}^2=\frac{16}{4}$

$I_{\text{max}}:I_{\text{min}}=16:4$

Final Answer: (d)