Wave Mechanics Question 721

Question: Two travelling waves $ y _{1}=A\sin

[k(x-c,t)] $ and $ y _{2}=A\sin [k(x+c,t)] $ are superimposed on string. The distance between adjacent nodes is [IIT 1992]

Options:

A) $ c,t/\pi $

B) $ c,t/2\pi $

C) $ \pi /2k $

D) $ \pi /k $

Show Answer

Answer:

Correct Answer: D

Solution:

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