Question

In a large room, a person receives direct sound waves from a source $120m$ away from him. He also receives waves from the same source after being reflected from the $25m$ high ceiling, at a point halfway between them. The two waves interfere constructively for a wavelength of

• A. $20,\frac{20}{3},\frac{20}{5},etc$
• B. $10,5,2.5,etc$
• C. $10,20,30,etc$
• D. $15,25,35,etc$

Answer 1

Answer: (A)

Path difference between the waves


$\Delta x=130-120=10m$
As phase between the two waves is $\pi$ because reflection takes place from the rigid end, so for constructive interference.
$\Delta x=\left(2n+1\right)\frac{\lambda }{2}$
$10=\left(2n+1\right)\frac{\lambda }{2}$
$\therefore \lambda =\frac{20}{2n+1}$
$n=0,{\lambda }_1=20m$
$n=1,{\lambda }_2=\frac{20}{3}m$
$n=2,{\lambda }_3=\frac{20}{5}m$