Question

Two waves having same amplitude $\left(A\right)$, wavelength $\left(\lambda \right)$ and frequency $\left(f\right)$ are propagating in the same direction. They interfere such that the amplitude of resultant wave is zero. The path difference between two wave can be :

• A. $\lambda$
• B. $2\lambda$
• C. $\frac{3\lambda }{2}$
• D. $\frac{3\lambda }{4}$

Answer 1

The correct option is C $\frac{3\lambda }{2}$

For the two waves having same amplitude, destructive interference results into minimum amplitude for the resultant wave.
$\Rightarrow A_{\text{resultant}}=|A_1-A_2|$
For the given zero resultant amplitude,
$\Rightarrow A_{\text{resultant}}=|A-A|=0$
It represents the case of destructive interference.
$\Rightarrow$Hence path difference between waves will be odd multiples of $\frac{\lambda }{2}$ i.e $\Delta x=\frac{\lambda }{2},\frac{3\lambda }{2},\frac{5\lambda }{2},..\text{etc}$
In a generalised form,
$\Rightarrow \Delta x=(2n+1)\frac{\lambda }{2}$
$\therefore \Delta x=\frac{3\lambda }{2}(\text{for}n=1)$
Option $\left(c\right)$ is correct.