In a medium, the phase difference between two particles separated by a distance $x$ is $\left(\frac{\pi}{5}\right)^{\circ}$. If the frequency of the oscillation of particles is $25 \mathrm{~Hz}$ and the velocity of propagation of the wave is $75 \mathrm{~m} / \mathrm{s}$, then the value of $x$ is

• A

  $0.1 \mathrm{~m}$
• B

  $0.2 \mathrm{~m}$
• Correct answer
  C

  $0.3 \mathrm{~m}$
• D

  $0.4 \mathrm{~m}$

Solution

The wavelength is related to velocity and frequency of the wave by following equation: The phase difference is given by $\phi=\frac{2 \pi}{\lambda} x$ $\begin{aligned} & \therefore \frac{\pi}{5}=\frac{2 \pi}{3} x \\ & \Rightarrow x=0.3 \mathrm{~m}\end{aligned}$

Hence, the correct answer is option: 'C'.