Question

Two periodic waves of intensities $I_1$ and $I_2$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

• A. $(\sqrt{I_1}-\sqrt{I_2})^2$
• B. $2(I_1+I_2)$
• C. $I_1+I_2$
• D. $(\sqrt{I_1}+\sqrt{I_2})^2$

Answer 1

The Correct Option is B

Other factors such as $\omega$ and $v$ remaining the
same, $I = A^2 \times$ constant $K$, or $A$
On superposition
$A_{max}=A_1+A_2$ and $A_{min}=A_{1}-A_{2}$
$\therefore \, \, \, \, A^2_{max}=A^2_2+2A_1A_2$
$\Rightarrow \frac{I_{max}}{K}=\frac{I_1}{K}+\frac{I_2}{K}+\frac{2\sqrt{I_1I_2}}{K}$
$A^2_{min}=A^2_1+A^2_ 2 -2A_1A_2$
$\Rightarrow \frac{I_{min}}{K}=\frac{I_1}{K}+\frac{I_2}{K}-\frac{2\sqrt{I_1I_2}}{K}$
$\therefore \, \, \, \, \, I_{max}+I_{min}=2I_1+2I_2 = 2(I_1+I_2)$