Wave Mechanics Question 700
Question: A wave represented by the given equation $ y=a\cos (kx-\omega ,t) $ is superposed with another wave to form a stationary wave such that the point x = 0 is a node. The equation for the other wave is
[IIT 1988; MP PMT 1994, 97; AIIMS 1998; SCRA 1998; MP PET 2001; KCET 2001; AIEEE 2002; UPSEAT 2004]
Options:
A) $ y=a\sin (kx+\omega ,t) $
B) $ y=-a\cos (kx+\omega ,t) $
C) $ y=-a\cos (kx-\omega ,t) $
D) $ y=-a\sin (kx-\omega ,t) $
Show Answer
Answer:
Correct Answer: B
Solution:
Since the point $ x=0 $ is a node and reflection is taking place from point $ x=0. $ This means that reflection must be taking place from the fixed end and hence the reflected ray must suffer an additional phase change of p or a path change of $ \frac{\lambda }{2} $ . So, if $ {y _{incident}}=a\cos (kx-\omega ,t) $
Therefore $ {y _{reflected}}=a\cos (-kx-\omega ,t+\pi ) $
$ =-a\cos (\omega ,t+kx) $
BETA
