Question

A sound source emits two sinusoidal sound waves, both of wavelength $\lambda$, along paths $A$ and $B$. The sound travelling along the path $B$ is reflected from four surfaces and then merges at point $Q$ while sound travelling along the path $A$ goes straight to point $Q$, producing minimum intensity at point $Q$ due to superposition. The minimum value of $d$ in terms of $\lambda$ will be
(Assume that the sound wave is not undergoing any phase change due to reflection)

• A. $\frac{\lambda }{8}$
• B. $\frac{\lambda }{4}$
• C. $\frac{\lambda }{5}$
• D. $\frac{\lambda }{2}$

Answer 1

The correct option is A $\frac{\lambda }{8}$


The path difference between the sound travelling along path $A$ and $B$,
$\Delta x=(2d+2d+d+d+d)-\left(3d\right)=4d$
For minimum intensity,
$\Delta x=(n+\frac{1}{2})\lambda$
For the minimum value of $d$,
$\Delta x=\frac{\lambda }{2}$
So, $4d=\frac{\lambda }{2}$
$\Rightarrow d=\frac{\lambda }{8}$