Question

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

• A. 0.2
• B. 0.1
• C. 0.5
• D. 0.4
• E. None of these

Answer 1

Answer: (B)

As, $v = n \lambda$
$\therefore \lambda = \frac{v}{n} = \frac{300}{500} = \frac{3}{5} \, m$
Now, phase difference =$\frac{2 \pi}{\lambda} \times$ path difference
$\therefore 66^{\circ} = \frac{2 \pi}{\lambda} \times $ path difference
or $\frac{60^{\circ} \times \pi}{180^{\circ}} = \frac{2 \pi \times 5}{3} \times x$ path difference
Path difference =$\frac{3 \times 60 \times \pi}{2 \pi \times 5 \times 180} = 0.1$