Question

Two waves of equal amplitude $\left(A\right)$, frequency $\left(f\right)$ and intensity $\left(I\right)$ propagate along the same direction in a medium. The intensity of resultant wave will be:

• A. $0$
• B. $2I$
• C. $4I$
• D. Between $0\text{and}4I$

Answer 1

The correct option is D Between $0\text{and}4I$

When two waves having equal amplitude $\left(A\right)$, frequency and intensity $\left(I\right)$ interfere,
$A_{\text{max}}=A_1+A_2=2A$
$A_{\text{min}}=A_1-A_2=0$
$\Rightarrow A_{\text{resultant}}$ will lie between $0\text{and}2A$
The intensity of wave is,
$I\propto A^2$
Since wave of amplitude $A$ has intensity $I$,
$I=k{A}^2$
For wave of amplitude $2A$,
$I_{\text{max}}=k\left(4A^2\right)=4k{A}^2=4I$
Minimum intensity will correspond to destructive interference,
$I_{\text{min}}=0$
$\Rightarrow I_{\text{resultant}}$ will lie between $0\text{and}4I$