Question

A sound source emits two sinusoidal sound waves. both of wavelength $\lambda$, along paths $A$ and $B$ as shown in figure. The sound travelling along path $B$ is reflected from five surfaces as shown and then merges at point $Q$, producing minimum intensity at that point. Find the minimum value of $d$ in terms of $\lambda$.

Answer 1

distance travelled along both$A=2d+d=3d$

now distance travelled along both

$B=2d+2d+d+d+d=7d$

both difference$=7d-3d=4d$

now,intensity of sound is minimum at pointQ,

which means they cancel out each other.

$\therefore$path difference$=(2x+1)\frac{\lambda }{2}$

for minimum case path difference$=\frac{\lambda }{2}or4d=\frac{\lambda }{2}d=\frac{\lambda }{8}$.