Question

In a large room, a person receives direct sound waves from a source $120 \, m$ away from him. He also receives waves from the same source after being reflected from the $25 \, m$ 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


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