Question

Two points on a travelling wave, having frequency $500 \, Hz$ and velocity $300 \, m \, s^{- 1}$ , are $60^\circ $ out of phase. The minimum distance between the two points is

• A. $\text{0.2}$
• B. $\text{0.1}$
• C. $\text{0.5}$
• D. $\text{0.4}$

Answer 1

Answer: (B)

$v=n\lambda $
$\therefore \, \lambda =\frac{v}{n}=\frac{300}{500}=\frac{3}{5}m$
Now, phase difference
$=\frac{2 \pi }{\lambda }\times \text{path difference}$
$\therefore \, \, \, \frac{\pi }{3}=\frac{2 \pi }{\lambda }\times \text{path difference} \, $
$or \, \, \, \frac{\pi }{3}=\frac{2 \pi \times 5}{3}\times \text{path difference}$
$\text{path difference}=\frac{3 \times 60 \times \pi }{2 \pi \times 5 \times 180}=0.1m$