The phase difference between two points separated by $0.8\text{ m}$ in a wave of frequency $120\text{ Hz}$…

The phase difference between two points separated by $0.8\text{ m}$ in a wave of frequency $120\text{ Hz}$ is $0.5\pi$. The velocity of wave will be
  1. $720\text{ ms}^{-1}$
  2. $384\text{ ms}^{-1}$
  3. $256\text{ ms}^{-1}$
  4. $144\text{ ms}^{-1}$

Solution

Phase difference, $\Delta\phi = \frac{2\pi}{\lambda} \cdot \Delta x \Rightarrow \lambda = \left(\frac{2\pi}{0.5\pi}\right)(0.8) = 3.2\text{ m}$ $\therefore$ Velocity of wave, $v = f\lambda = 120 \times 3.2 = 384\text{ ms}^{-1}$

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