The equation of a stationary wave is $y = 0.8 \cos \left( \frac{\pi x}{20} \right) \sin 200\pi t$, where $x$…

The equation of a stationary wave is $y = 0.8 \cos \left( \frac{\pi x}{20} \right) \sin 200\pi t$, where $x$ is in cm and $t$ is in second. The separation between consecutive nodes will be
  1. $20\text{ cm}$
  2. $10\text{ cm}$
  3. $40\text{ cm}$
  4. $30\text{ cm}$

Solution

Given, $k = \frac{2\pi}{\lambda} = \frac{\pi}{20} \Rightarrow \lambda = 40\text{ cm}$ Separation between two consecutive nodes $= \frac{\lambda}{2} = \frac{40}{2} = 20\text{ cm}$

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