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

In a medium in which a transverse progressive wave travelling, the phase difference between the points with a separation of $1.25\text{ cm}$ is $\frac{\pi}{4}$. If the frequency of wave is $1000\text{ Hz}$, the velocity in the medium is [EAMCET 2015]
  1. $10^4\text{ ms}^{-1}$
  2. $125\text{ ms}^{-1}$
  3. $100\text{ ms}^{-1}$
  4. $10\text{ ms}^{-1}$

Solution

Given, $\text{path difference} = 1.25\text{ cm} = 1.25 \times 10^{-2}\text{ m}$ $\text{Phase difference} = \frac{\pi}{4}$ $\text{Frequency}, n = 1000\text{ Hz}$ As, $\text{phase difference} = \frac{2\pi}{\lambda} (\text{path difference})$ $\Rightarrow \frac{\pi}{4} = \frac{2\pi}{\lambda} \times 1.25 \times 10^{-2}$ $\Rightarrow \lambda = 2 \times 4 \times 1.25 \times 10^{-2}$ $\therefore \text{Wavelength}, \lambda = 10 \times 10^{-2} = \frac{1}{10}\text{ m}$ $\text{Velocity of wave}, v = f\lambda$ $\Rightarrow v = 1000 \times \frac{1}{10} = 100\text{ ms}^{-1}$

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