Question

The superposing waves are represented by the following equations
$y_{1}=5 \sin 2 \pi(10 t-0.1 x), y_{2}=10 \sin 2 \pi(20 t-0.2 x)$ Ratio of intensities $\frac{I_{\max }}{I_{\min }}$ will be:

• A. 1
• B. 9
• C. 4
• D. 16

Answer 1

Answer: (B)

Given that
$a_{1}=5,\, a_{2}=10$
$\Rightarrow \frac{I_{\max }}{I_{\min }}=\frac{\left(a_{1}+a_{2}\right)^{2}}{\left(a_{1}-a_{2}\right)^{2}}$
$=\left(\frac{5+10}{5-10}\right)^{2}=\frac{9}{1}$.