Question

Two superimposing waves are represented by equation $y_1=2\sin 2\pi (10t-0.4x)$ and $y_2=4\sin 2\pi (20t-0.8x)$. The ratio of $I_{max}$ to $I_{min}$

• A. $36:4$
• B. $25:9$
• C. $1:4$
• D. $4:1$

Answer 1

The correct option is A $36:4$

$y_1=2sin2x(10t-0.4x)$

$y_2=4sin2x(20t-0.8x)$

Now, we know that,

$\frac{I_{max}}{I_{min}}=(\frac{a_1+a_2}{a_1-a_2}{)}^2$

From above, $a_1=2,a_2=4$

$\Rightarrow \frac{I_{max}}{I_{min}}=\frac{6^2}{(-2{)}^2}=\frac{36}{4}$

Hence, ratio of $I_{max}$ to $I_{min}$ is $36:4.$