Question

In a large room, a person receives direct sound waves from a source $120m$ away from him. He also receives waves from the $25m$ high ceiling at a point half way between them. The two waves interfere constructively for wavelengths of

• A. $20m,20/3m,20/5m$
• B. $10m,20m,30m,etc.$
• C. $10cm,5m,10/3m,etc.$
• D. $15m,25m,35m,etc.$

Answer 1

The correct option is C $10cm,5m,10/3m,etc.$

Path difference is $\Delta x$
$\Delta x=2\left[\sqrt{{25}^2+{60}^2}\right]-120=10$

phase change $\delta =\frac{2\pi }{\lambda }\Delta x$
Constructive interference for $\delta =2n\pi$, where $n=1,2,3$ etc.
Thus, ${\lambda }_1=10$ for $n=1$

${\lambda }_2=5$ for $n=2$

${\lambda }_3=10/3$ for $n=3$ etc.