Wave Mechanics Question 667
Question: 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
Options:
A) $ ct/\pi $
B) $ ct/2\pi $
C) $ \pi /2k $
D) $ \pi /k $
Show Answer
Answer:
Correct Answer: D
Solution:
[d] $ y=A\sin (kx-kct)+A\sin (kx+kct) $
$ =2,A,\sin $
$ ( \frac{kx-kct+kx+kct}{2} ).\cos ( \frac{kx-kct-kx-kct}{2} ) $
$ =2,A,\sin (kct).cos,kx. $ Thus $ \frac{2\pi }{\lambda }=k $ ,
$ \
Therefore \lambda =\frac{2\pi }{k} $ The distance between adjacent nodes $ =\frac{\lambda }{2}=\frac{\pi }{k} $
BETA
