Question

The ratio of maximum and minimum intensities of two sources is $4:1.$ The ratio of their amplitudes is-

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

Answer 1

The correct option is B $3:1$

Given,

$\frac{I_{max}}{I_{min}}=\frac{4}{1}$

As we know $I\propto (\text{Amplitude}{)}^2$

$\therefore \frac{I_{max}}{I_{min}}=\frac{A_{max}^2}{A_{min}^2}$

$\frac{I_{max}}{I_{min}}=\frac{[A_1+A_2{]}^2}{[A_1-A_2{]}^2}$

$\frac{4}{1}={\left(\frac{\frac{A_1}{A_2}+1}{\frac{A_1}{A_2}-1}\right)}^2$

$\frac{2}{1}=\frac{\frac{A_1}{A_2}+1}{\frac{A_1}{A_2}-1}$

$2\left(\frac{A_1}{A_2}\right)-2=\frac{A_1}{A_2}+1$

$\therefore \frac{A_1}{A_2}=\frac{3}{1}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.