In a medium in which a transverse progressive wave is travelling, the phase difference between two points…

In a medium in which a transverse progressive wave is travelling, the phase difference between two points with a separation of $1.25\text{ cm}$ is $\left(\frac{\pi}{3}\right)$. If the frequency of wave is $1000\text{ Hz}$, its velocity will be
  1. $75\text{ ms}^{-1}$
  2. $125\text{ ms}^{-1}$
  3. $100\text{ ms}^{-1}$
  4. $50\text{ ms}^{-1}$

Solution

Phase difference, $\Delta \phi = \frac{2\pi}{\lambda} \cdot \Delta x$ or $\lambda = \frac{2\pi}{\Delta \phi} \cdot \Delta x = \frac{2\pi}{(\pi / 3)} \times 1.25 \times 10^{-2}\text{ m} = 7.5 \times 10^{-2}\text{ m}$ Velocity, $v = f \lambda = 1000 \times 7.5 \times 10^{-2} = 75\text{ ms}^{-1}$

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