Question

Two coherent waves represented by $y_1=A\text{sin}(\frac{2\pi x_1}{\lambda }-\omega t+\frac{\pi }{6})$ and ${\lambda }_2=A\text{sin}(\frac{2\pi x_2}{\lambda }-\omega t+\frac{\pi }{8})$ are superposed. The path difference $(x{­}_1-x_2)$ to produce constructive interference $\left(nϵI\right)$.

• A. $n\lambda$
• B. $(n-\frac{1}{48})\lambda$
• C. $(n-48)\lambda$
• D. $\frac{n\lambda }{2}$

Answer 1

The correct option is B

$(n-\frac{1}{48})\lambda$

$=(\frac{2\pi x_1}{\lambda }-\omega t+\frac{\pi }{6})-(\frac{2\pi x_2}{\lambda }-\omega t+\frac{\pi }{8})=2\pi n$

$\Rightarrow X_1-X_2=(n-\frac{1}{48})\lambda$