Question

Two travelling waves $y_1=Asin\left[k\right(x+ct\left)\right]$ and $y_2=Asin\left[k\right(x-ct\left)\right]$ are superposed on a string. The distance between adjacent nodes is

• A. $\frac{ct}{\pi }$
• B. $\frac{ct}{2\pi }$
• C. $\frac{\pi }{2k}$
• D. $\frac{\pi }{k}$

Answer 1

The correct option is D $\frac{\pi }{k}$

Distance between adjacent nodes $=\frac{\lambda }{2}$.
Also, $\frac{2\pi }{\lambda }=$ Coefficient of x in the argument of the sine function = k
$\Rightarrow \lambda =\frac{2\pi }{k}$
Hence, the distance between adjacent nodes $=\frac{\pi }{k}$ and the correct choice is (d).