Question

Two points on a travelling wave, having frequency $500Hz$ and velocity $300m{s}^{-1}$ , 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
$=\frac{2\pi }{\lambda }\times \text{path difference}$
$\therefore \frac{\pi }{3}=\frac{2\pi }{\lambda }\times \text{path difference}$
$or\frac{\pi }{3}=\frac{2\pi \times 5}{3}\times \text{path difference}$
$\text{path difference}=\frac{3\times 60\times \pi }{2\pi \times 5\times 180}=0.1m$