Two travelling waves $y_1 = A \sin [k (x - ct)]$ and $y_2 = A \sin [k (x + ct)]$ are superimposed on string.…

Two travelling waves $y_1 = A \sin [k (x - ct)]$ and $y_2 = A \sin [k (x + ct)]$ are superimposed on string. The distance between adjacent nodes is
  1. $\frac{c}{\pi}$
  2. $\frac{c}{2\pi}$
  3. $\frac{\pi}{2k}$
  4. $\frac{\pi}{k}$

Solution

The distance between adjacent nodes, $x = \frac{\lambda}{2} \Rightarrow \lambda = 2x$ Also, $k = \frac{2\pi}{\lambda}$ Hence, $x = \frac{\pi}{k}$

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