• # question_answer Two points are located at a distance of 10 m and 15 m from the source of oscillation. The period of oscillation is 0.05 s and the velocity of the wave is $300\,\,m{{s}^{-1}}$. What is the phase difference between the oscillations of two points? A)  $\frac{\pi }{3}$                                 B)  $\frac{2\pi }{3}$ C)  $\pi$                          D)  $\frac{\pi }{6}$

Path difference between two points $\Delta x=15-10=5\,\text{m}$ Time period, $T=0.5\,s\Rightarrow$ frequency $v=\frac{1}{T}=\frac{1}{0.05}=20\,\,Hz$ Velocity, $v=300\,\,\text{m}{{\text{s}}^{-1}}$ $\therefore$ Wavelength, $\lambda =\frac{v}{v}=\,\frac{300}{20}=15\,m$ Hence, phase difference $\Delta \phi =\frac{2\pi }{\lambda }\times \Delta x=\frac{2\pi }{15}\times 5=\frac{2\pi }{3}$